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Slope Worksheets

The slope (or gradient) of a line is a number that denotes the 'steepness' of the line, also commonly called 'rise over run'. Knowledge of relevant formulae is a must for students of grade 6 through high school to solve some of these pdf worksheets. This page consists of printable exercises like introduction to slopes such as identifying the type and counting the rise and run; finding the slope using ratio method, slope-intercept formula and two-point formula; drawing lines through coordinates and much more! Employ our free worksheets to sample our work. Answer keys are included.

Printing Help - Please do not print slope worksheets directly from the browser. Kindly download them and print.

Identify the Types of Slopes

Identify the Types of Slopes

Introduction to slopes: Based on the position of the line on the graph, identify the type of slope - positive, negative, zero or undefined. This exercise is recommended for 6th grade and 7th grade children.

  • Download the set

Draw Lines on a Graph: Types of Slopes

Draw Lines on a Graph: Types of Slopes

The first part of worksheets require students to plot the points on the graph, draw the line and identify the type of slope. In the next section, draw a line through the single-point plotted on the graph to represent the type of slope mentioned.

Count the Rise and Run - Level 1

Count the Rise and Run

Based on the two points plotted on a graph, calculate the rise and run to find the slope of the line in the first level of worksheets. Find the rise and run between any two x- and y- coordinates on the line provided in the second level of worksheets. This practice resource is ideal for 7th grade and 8th grade students.

Graph the Line

Graph the Line

Draw a line through a point plotted on the graph based on the slope provided in this set of pdf worksheets which is suitable for 9th grade children.

Fun Activity: Slope of the Roof

Fun Activity: Slope of the Roof

This set of fun activitiy worksheets contains houses with roofs of various sizes. Find the slope of the roof of each house. Answers must be in the form of positive slopes.

Find the Slope: Ratio Method

Find the Slope: Ratio Method

Use the x- and y- coordinates provided to find the slope (rise and run) of a line using the ratio method. A worked out example along with the formula is displayed at the top of each worksheet for easy reference.

Find the Slope: Line segments in a Triangle

Find the Slope: Line segments in a Triangle

Triangles are represented on each graph in this assembly of printable 8th grade worksheets. Learners will need to identify the rise and run for each of the three line segments that are joined to form a triangle.

Two-Point Formula

Two-Point Formula

Employ the two-point formula that is featured atop every worksheet along with a worked out example. Substitute each pair of x- and y- coordinates in the given formula to find the slope of a line.

Plot the Points and Find the Slope

Plot the Points and Find the Slope

Plot the points on the graph based on the x- and y-coordinates provided. Then, find the slope of each line, so derived. Some problems contain x- and y-intercepts as well.

Find the Missing Coordinates

Find the Missing Coordinates

In this series of high school pdf worksheets, the slope and the co-ordinates are provided. Use the slope formula to find the missing coordinate.

Slope-Intercept Form

Slope-Intercept Form

This set of printable worksheets features linear equations. Students are required to find the slopes by writing linear equations in slope-intercept form.

Related Worksheets

» Point-Slope Form

» Slope-Intercept Form

» Two-Point Form

» Equation of a Line

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How to Calculate the Slope of a Line

Last Updated: November 2, 2023 Fact Checked

Finding the Slope

Types of slopes, expert interview.

This article was co-authored by Grace Imson, MA and by wikiHow staff writer, Johnathan Fuentes . Grace Imson is a math teacher with over 40 years of teaching experience. Grace is currently a math instructor at the City College of San Francisco and was previously in the Math Department at Saint Louis University. She has taught math at the elementary, middle, high school, and college levels. She has an MA in Education, specializing in Administration and Supervision from Saint Louis University. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 551,621 times.

If you’re taking algebra, finding the slope of a line is an important concept to understand. But there are multiple ways to find the slope, and your teacher may expect you to learn them all. Feeling a bit overwhelmed? Don’t fret. This guide explains how to find the slope of a line using ( x , y ) points from graphs. We’ll also explain how the slope formula works, and how to recognize positive, negative, zero, and undefined slopes. Keep reading to learn how to calculate the slope of a line and ace your next quiz, exam, or homework assignment.

Practice Problems

geometry assignment find the slope of each line

Things You Should Know

  • Slope = Rise divided by Run and is represented by the variable m . The slope m is found in the slope-intercept formula, y = mx + b
  • When given two ( x , y ) points on a line, Run = x 2 - x 1 and Rise = y 2 - y 1 . Therefore, m = ( y 2 - y 1 )/( x 2 - x 1 ).
  • Find the slope by finding two ( x , y ) points on a line, labeling one ( x 1 , y 1 ) and the other ( x 2 , y 2 ). The slope m = ( y 2 - y 1 )/( x 2 - x 1 ).

Step 1 This is the slope formula, which states Slope = Rise over Run.

  • The slope of a line is represented by the variable m . In this example, m = 2 .
  • The slope m is part of the formula y = mx + b . This is called the “slope-intercept formula.”
  • You can use y = mx + b to calculate a value of y that corresponds to a particular value of x . Each pair of corresponding x and y values is called a “point”, written as ( x , y ). [2] X Research source
  • If you find multiple ( x , y ) points for the same equation, you can plot those points on a graph and draw a straight line through them.

Step 2 Find two different points that the line passes through.

  • In the example above, we picked the points ( 2 , 1 ) and ( 5 , 3 ).
  • The first point has an x value of 2 and a y value of 1 , so it’s written as ( 2 , 1 ).
  • The second point has an x value of 5 and a y value of 3 . It’s written as ( 5 , 3 ).

Step 3 Choose one point to be (x1, y1) and the other to be (x2, y2).

  • For simplicity, you can always make the point farthest on the left ( x 1 , y 1 ). This point will have the lower value for x .
  • In reality, you can make either point ( x 1 , y 1 ) or ( x 2 , y 2 ), as long as you remember which is which.

Step 4 Calculate m by dividing the Rise by the Run.

  • ( x 1 , y 1 ) = ( 2 , 1 ), and ( x 2 , y 2 ) is ( 5 , 3 ).
  • Rise = y 2 - y 1 , or 3 - 1 . Run = x 2 - x 1 , or 5 - 2 .
  • Rise/Run = (3 - 1)/(5 - 2) , or (2/3) .
  • Therefore, m = ⅔ , or 0.67 .

Step 1 Positive slope:

  • A positive slope can be a positive integer like 3, 5, or 16. It can also be a fraction or decimal, like ½, 0.75, or 1.86.
  • Look closely at the y = mx + b formulas listed with each line. Notice that m is always a positive number.

Step 2 Negative slope:

  • A negative slope can be a negative integer like -2, -6, or -19. It can also be a negative fraction or decimal, like -⅓, -0.9, or -2.21.
  • Note the y = mx + b formulas for each line. You’ll see that m is always a negative number.

Step 3 Zero slope:

  • A horizontal line always has a slope of m = 0 . This means the equation y = mx + b can be written as y = 0x + b . Since 0x = 0 , the equation gets simplified to y = b , with b being the y corresponding value for all values of x .
  • The formulas for the line above all follow the same format: y = some number.

Step 4 Undefined slope:

  • The image above shows lines with undefined slopes.

Community Q&A

Donagan

  • You can calculate the slope from a list of ( x , y ) points that correspond to a line. Choose one point from the list to be ( x 1 , y 1 ) and another to be ( x 2 , y 2 ). Thanks Helpful 0 Not Helpful 1
  • As long as you have at least two ( x , y ) points, you don’t need to plot the line on a graph to calculate the slope (though your assignments may still require you to do so). Thanks Helpful 0 Not Helpful 0

geometry assignment find the slope of each line

You Might Also Like

Use Distance Formula to Find the Length of a Line

Thanks for reading our article! If you’d like to learn more about mathematics, check out our in-depth interview with Grace Imson, MA .

  • ↑ https://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut27_graphline.htm
  • ↑ https://www.alamo.edu/contentassets/ab5b70d70f264cec9097745e8f30ca0a/graphing/math0303-equations-of-a-line.pdf
  • ↑ https://web.ics.purdue.edu/~braile/eas100/Slope.pdf

About This Article

Grace Imson, MA

In geometry, the slope of a line describes how steep the line is, as well as the direction it’s going—that is, whether the line is going up or down. To find the slope of a line, all you have to do is divide the rise of the line by its run. To get the rise and run, pick any two coordinates along the line. For instance, your first coordinate might be at 2 on the x axis and 4 on the y axis, while your second coordinate might be at 5 on the x axis and 7 on the y axis. Next, write a fraction with the difference between your two y coordinates on top—this is the rise—and the difference between the x coordinates on the bottom—that’s the run. In our example, the rise would be 7-4, while the run would be 5-2. This means the slope of the line would be 3/3, or 1. To figure out the direction of the line, check whether your slope is positive or negative. Lines that go up from left to right always have a positive slope, while lines that go down from left to right always have a negative slope. To figure out how steep the line is, look at the magnitude of the number. Whether it’s positive or negative, the greater the magnitude, the steeper the slope. For instance, a line with a slope of -7 is steeper than a line with a slope of -2. Similarly, a line with a slope of 15 is steeper than a line with a slope of 3. If you want to learn how to reduce the numbers in your slope, keep reading the article! Did this summary help you? Yes No

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Straight line graphs

How to find the slope of a line

Here you will learn about the slope of a line, including how to calculate the slope of a straight line from a graph, from two coordinates and state the equations of horizontal and vertical lines.

Students will first learn about how to find the slope of a line as part of ratios and proportions in 7 th grade and functions in 8 th grade, and continue to work with slope in high school.

What is the slope of a line?

The slope of a line is a measure of how steep a straight line is. In the general equation of a line or slope intercept form of a line, y=m x+b, the slope is denoted by the coefficient m.

Imagine walking up a set of stairs. Each step has the same height and you can only take one step forward each time you move. If the steps are taller, you will reach the top of the stairs quicker, if each step is shorter, you will reach the top of the stairs more slowly.

Let’s look at sets of stairs,

US Webpages_ How to find the slope of a line 1 US

The blue steps are taller than the red steps and so the slope is steeper (notice the blue arrow is steeper than the red arrow).

The green steps are not as tall as the red steps so the slope is shallower (the green arrow is shallower than the red arrow).

Just like the example with the stairs above, slope can be thought of as a measure of the steepness of a line. The slope of a line can be positive or negative but is always observed from left to right.

US Webpages_ How to find the slope of a line 2 US

The linear relationship between two variables can be drawn as a straight line graph and the slope of the line calculates the rate of change between the two variables.

The rate of change is the slope of a line.

For example,

The exchange rate between two currencies can be represented by a linear relationship where the exchange rate represents the slope. When calculating the exchange rate of two currencies, you can calculate the slope of the line to find the rate of change between them.

Here, the exchange rate between pounds (£) and dollars (\$) is equal to \cfrac{3}{5}, for every 3 pounds there are 5 dollars. Let’s look at this linear relationship on the graph.

US Webpages_ How to find the slope of a line 3 US

In order to calculate the slope of a straight line given the two coordinates \left(x_1, y_1\right) and \left(x_2, y_2\right), you find:

  • The change in x is the difference between the x coordinates: x_2-x_1
  • The change in y is the difference between the y coordinates: y_2-y_1

The slope formula is:

It can be helpful to think about this formula as:

‘Change in y divided by change in x’ OR ‘Rise over run’

Let’s have a closer look at the slope of 4 lines

US Webpages_ How to find the slope of a line 4 US

  • When m=1, for each unit square you move to the right, you move 1 unit square upwards.
  • When m=2, for each unit square you move to the right, you move 2 unit squares upwards.
  • When m=- 3, for each unit square you move to the right, you move 3 unit squares downwards.
  • When m=\cfrac{1}{2}, for each unit square you move to the right, you move \cfrac{1}{2} a unit square upwards.

How far apart do the coordinates you choose need to be?

Let us look at the example of m=2.

US Webpages_ How to find the slope of a line 5 US

  • The first blue line has a slope of m=\cfrac{2}{1}=2.
  • The second blue line has a slope of m=\cfrac{6}{3}=2.
  • The third blue line has a slope of m=\cfrac{10}{5}=2.

No matter how far apart the coordinates are on the line, the slope \cfrac{y_2-y_1}{x_2-x_1} will always simplify to the same number, here m=2.

Tip: Use two coordinates that cross the corners of two grid squares so that you can accurately measure the horizontal and vertical distance between them. Use integers as much as possible!

Remember: the change in x is horizontal, the change in y is vertical.

Let’s look at horizontal and vertical lines.

Let us look at a couple of examples to further understand the equations of horizontal and vertical lines.

US Webpages_ How to find the slope of a line 6 US

In the diagram above, all the coordinates share an x value of 4, regardless of the y value, so if you join the coordinates together to make a straight line, you get the vertical line with the equation x=4. Notice the line crosses the x -axis at (4,0) (the x -intercept is 4 ). Vertical lines have an undefined slope.

You can also use the formula for slope on vertical lines. Using the points (4,1) and (4, -3), substitute the values into the formula, \cfrac{y_2-y_1}{x_2-x_1}.

Now let’s look at horizontal lines.

US Webpages_ How to find the slope of a line 7 US

In the diagram above, all the coordinates share a y value of 2, regardless of the x value, so if you join the coordinates together to make a straight line, you get the horizontal line with the equation y=2. Notice the line crosses the y -axis at (0,2) (the y -intercept is 2 ). Horizontal lines have a slope of 0.

You can also use the formula for slope on horizontal lines. Using the points (-2, 2) and (4, 2), substitute the values into the formula, \cfrac{y_2-y_1}{x_2-x_1}.

All vertical lines are of the form x=a and all horizontal lines are of the form y=b where a and b can be any number.

The x axis is a horizontal line and the y axis is a vertical line. So, you can represent them with equations.

The equation y=0 is where you draw the x -axis as the line y=0 is horizontal and crosses the y -axis at 0. The y-axis is drawn using the equation x=0 as this line is vertical and crosses the x -axis at 0.

What is the slope of a line?

Common Core State Standards

How does this relate to 7 th grade math and 8 th grade math?

  • Grade 7 – Ratios and Proportional Relationships (7.RP.A.2b) Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.
  • Ratios and Proportional Relationships (7.RP.A.2e) Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
  • Grade 8 – Functions (8.F.A.3) Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
  • Grade 8 – Expressions and Equations (8.EE.B.5) Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
  • High School: Algebra – Reasoning with Equations and Inequalities (HSA.REI.B.3) Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • High School Algebra – Creating Equations (HSA-CED.A.2) Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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How to calculate the slope of a line

In order to calculate the slope of a line:

Select two points on the line.

Sketch a right angled triangle and label the change in \textbf{y} and the change in \textbf{x} .

Divide the change in \textbf{y} by the change in \textbf{x} to find \textbf{m} .

How to find the slope of the line examples

Example 1: using a straight line graph (positive slope).

Calculate the slope of the line:

US Webpages_ How to find the slope of a line 8 US

2 Sketch a right angled triangle and label the change in \textbf{y} and the change in \textbf{x} .

US Webpages_ How to find the slope of a line 10 US

3 Divide the change in \textbf{y} by the change in \textbf{x} to find \textbf{m} .

Here, \cfrac{4}{2}=2 so m=2.

Example 2: using a straight line graph (negative slope)

Calculate the slope given the graph of the line:

US Webpages_ How to find the slope of a line 11 US

Remember the height of the triangle represents the change in y, and the base of the triangle represents the change in x.

Looking at the coordinate (1,2), to get to the coordinate (5,-4) you have to add 4 to the x coordinate, and subtract 6 from the y coordinate.

Although the height of a triangle is always positive, you are calculating the change in y, so you must write the change in y as -6.

Here, \cfrac{-6}{4}=-\cfrac{3}{2} so m=-\cfrac{3}{2}.

Example 3: using a straight line graph with two coordinates (positive slope)

US Webpages_ How to find the slope of a line 14 US

Here you already have this information, so you can continue on with step 2.

US Webpages_ How to find the slope of a line 15 US

Here, \cfrac{5}{5}=1 so m=1.

Example 4: find the slope of the line given two points

US Webpages_ How to find the slope of a line 16 US

Here you have to be careful because each grid square has a base of 1 unit but a height of 2 units. This means that the distance between the y coordinates (the change in y ) is equal to -8-8=-16.

Here, \cfrac{-16}{1}=-16, so m=-16.

Example 5: given two coordinates (positive slope)

Calculate the slope of the line with coordinates A(4,3) and B(7,12).

Here you have the two coordinates A(4,3) and B(7,12) without a graph to visualize the line. You therefore need to determine whether the line has a positive or negative slope as well as the value for m.

As there is no right angle to sketch, you will solve algebraically by calculating the change in y and the change in x.

\\y_{2}-y_{1}=12-3=9\\

\\x_{2}-x_{1}=7-4=3\\

Top tip: make sure you always subtract one coordinate from the other. Here you subtracted the values from coordinate A from coordinate B. Do not mix up the order.

Example 6: given two coordinates (negative slope)

Calculate the slope of the line with coordinates P(-10,-3) and Q(2,-7).

Here you have the two coordinates P(-10,-3) and Q(2,-7) without a graph to visualize the line. You therefore need to determine whether the line has a positive or negative slope as well as the value for m.

\\y_{2}-y_{1}=-7--3=-7+3=-4\\

\\x_{2}-x_{1}=2--10=2+10=12\\

m=-\cfrac{1}{3}

Teaching tips for how to find the slope of a line

  • Give students plenty of time to work with slope on a graph before moving to manipulating coordinates algebraically to find the slope.
  • Let students use a graphing calculator or digital graphing platforms such as Desmos to explore how changing a slope changes the slope of a line. For example, have them graph y=-2 x+3, \, y=2 x+3, \, y=-\cfrac{1}{2} x+3 and y=\cfrac{1}{2} +3 and ask them to compare and contrast the slopes with each other.

Easy mistakes to make

  • The change in x is x_2-x_1
  • The change in y is y_2-y_1
  • Incorrectly simplifying m with negative number division When you subtract one coordinate from another, one or both of the numerator and the denominator can be negative. If one is negative, the slope is negative. If both are negative, remember a negative number divided by another negative number is a positive number, so the slope is positive. For example, \cfrac{6}{-2}=\cfrac{-6}{2}=-3 or \cfrac{-8}{-4}=\cfrac{8}{4}=2
  • Dividing the change in \textbf{x} by the change in \textbf{y} It is easy to mistake the calculation of m to be the change in x divided by the change in y. This would result in the reciprocal of the slope which, most of the time (not always) is incorrect.
  • Reading scales incorrectly Sometimes the scale of the axis can change. For example, 1 square can be a half unit, or 2 units, etc. For this reason, it is important to use the coordinates and the axes to make sure these values are correct. Example 4 highlights this fact as each square on the y -axis is 2 units.

Related straight line graphs lessons

  • Graphing linear equations
  • How to find the midpoint
  • Distance formula
  • How to find the y intercept and the the x intercept
  • Linear interpolation

Practice how to find the slope of a line questions

1. Calculate the slope of the line:

US Webpages_ How to find the slope of a line 18 US

The change in x is +5. The change in y is +2.

US Webpages_ How to find the slope of a line 20 US

2. Calculate the slope of the line:

US Webpages_ How to find the slope of a line 21 US

The change in x is +14. The change in y is -9.

US Webpages_ How to find the slope of a line 23 US

3. Calculate the slope of the line given the coordinates:

US Webpages_ How to find the slope of a line 24 US

Notice, each square on the x -axis is 2 units.

The change in x is +6.  The change in y is +8.

US Webpages_ How to find the slope of a line 25 US

4. Calculate the slope of the line given the coordinates:

US Webpages_ How to find the slope of a line 26 US

Notice, each square on the x -axis is \cfrac{1}{2} a unit.

The change in x is +6. The change in y is -3.

US Webpages_ How to find the slope of a line 27 US

5. Calculate the slope of the line given the coordinates A(2,6) and B(8,24).

6. Calculate the slope of the line given the coordinates A(-3,-8) and B(-5,10)

How to find the slope of the line FAQs

Yes, because they both represent a rate of change or steepness of a line. So, you can either count the vertical distance and the hortizontal distance between two points (rise over run) or you can use the formula for slope, \cfrac{y_2-y_1}{x_2-x_1}.

There are different ways to write the equation of the line. Some of the most popular forms are point-slope form, standard form, and slope-intercept form.

The gradient is another name of slope. It is the change in y over the change in x.

Lines that are parallel have the same slope, which is why they never intersect. You can tell two lines are parallel by looking at the slope of a given line and seeing if the other line has the same m value.

Lines that are perpendicular have slopes that are opposite reciprocals. You can tell two lines are perpendicular by looking at their slope equations and seeing if the m values are opposite reciprocals.

The next lessons are

  • Angles in parallel lines
  • Angels in polygons
  • Rate of change
  • Systems of equations
  • Number patterns

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The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass.

The slope of any line can be calculated using any two distinct points lying on the line. The slope of a line formula calculates the ratio of the "vertical change" to the "horizontal change" between two distinct points on a line. In this article, we will understand the method to find the slope and its applications.

What is Slope?

The slope of a line is defined as the change in y coordinate with respect to the change in x coordinate of that line . The net change in y coordinate is Δy, while the net change in the x coordinate is Δx. So the change in y coordinate with respect to the change in x coordinate can be written as,

Introduction to Slope of a Line | The slope of line is the measure of steepness or the direction of line the coordinate plane.

m = Δy/Δx where, m is the slope

Note that tan θ = Δy/Δx

We also refer this tan θ to be the slope of the line.

Slope of a Line

The slope of the line is the ratio of the rise to the run , or rise divided by the run. It describes the steepness of line in the coordinate plane . Calculating the slope of a line is similar to finding the slope between two different points. In general, to find the slope of a line, we need to have the values of any two different coordinates on the line.

Slope Between Two Points

The slope of a line can be calculated using two points lying on the straight line . Given the coordinates of the two points, we can apply the slope of line formula. Let coordinates of those two points be, P 1 = (x 1 , y 1 ) P 2 = (x 2 , y 2 )

As we discussed in the previous sections, the slope is the "change in y coordinate with respect to the change in x coordinate of that line". So, putting the values of Δy and Δx in the equation of slope, we know that: Δy = y 2 - y 1 Δx = x 2 - x 1

Hence, using these values in a ratio, we get :

Slope = m = tan θ = (y 2 - y 1 )/(x 2 - x 1 )

where, m is the slope, and θ is the angle made by the line with the positive x-axis.

Slope of a Line Formula

The slope of a line can be calculated from the equation of the line. The general slope of a line formula is given as,

  • m is the slope, such that m = tan θ = Δy/Δx
  • θ is the angle made by the line with the positive x-axis
  • Δy is the net change in y-axis
  • Δx is the net change in x-axis

Slope of a Line Example

Let us recall the definition of slope of a line and try solving the example given below.

Example: What is the equation of a line whose slope is 1, and that passes through the point (-1, -5) ?

We know that if the slope is given as 1, then the value of m will be 1 in the general equation y = mx + b. So, we substitute the value of m as 1, and we get,

Now, we already have the value of one point on the line. So, we put the value of the point (-1, -5) in the equation y = x + b, and we get,

Hence, substituting the values of m and b in the general equation, we get our final equation as y = x - 4.

Equation is: y = x - 4

How to Find Slope?

We can find the slope of the line using different methods. The first method to find the value of the slope is by using the equation is given as,

m = (y 2 - y 1 )/(x 2 - x 1 ) where, m is the slope of the line.

Also, the change in x is run and the change in y is rise or fall . Thus, we can also define a slope as, m = rise/run

Finding Slope from a Graph

While finding the slope of a line from the graph, one method is to directly apply the formula given the coordinates of two points lying on the line. Let's say the values of the coordinates of the two points are not given. So, we have another method as well to find the slope of the line. In this method, we try to find the tangent of the angle made by the line with the x-axis. Hence, we find the slope as given below.

Finding slope of a line - Slope of a line by using Angle

The slope of a line has only one value. So, the slopes found by Methods 1 and 2 will be equal. In addition to that, let's say we are given the equation of a straight line. The general equation of a line can be given as,

The value of the slope is given as m; hence the value of m gives the slope of any straight line.

The below-given steps can be followed to find the slope of a line such that the coordinates of two points lying on the line are: (2, 4), (1, 2)

  • Step 1: Note the coordinates of the two points lying on the line, (x 2 , y 2 ), (x 1 , y 1 ). Here the coordinates are given as (2, 4), (1, 2).
  • Step 2: Apply the slope of line formula, m = (y 2 - y 1 )/(x 2 - x 1 ) = (4 - 2)/(2 - 1) = 2.
  • Step 3: Therefore, the slope of the given line = 2.

Types of Slope

We can classify the slope into different types depending upon the relationship between the two variables x and y and thus the value of the gradient or slope of the line obtained. There are 4 different types of slopes, given as,

  • Positive slope
  • Negative slope

Undefined Slope

Positive slope.

Graphically, a positive slope indicates that while moving from left to right in the coordinate plane , the line rises, which also signifies that when x increases, so do y.

Negative Slope

Graphically, a negative slope indicates that while moving from left to right in the coordinate plane, the line falls, which also signifies that when x increases, y decreases.

For a line with zero slope , the rise is zero, and thus applying the rise over run formula we get the slope of the line as zero.

For a line with an undefined slope, the value of the run is zero. The slope of a vertical line is undefined.

Slope of Horizontal Line

We know that, a horizontal line is a straight line that is parallel to the x-axis or is drawn from left to right or right to left in a coordinate plane. Therefore, the net change in the y-coordinates of the horizontal line is zero. The slope of a horizontal line can be given as,

Slope of a horizontal line, m = Δy/Δx = zero

Slope of Vertical Line

We know that, a vertical line is a straight line that is parallel to the y-axis or is drawn from top to bottom or bottom to top in a coordinate plane. Therefore, the net change in the x-coordinates of the vertical line is zero. The slope of a vertical line can be given as,

Slope of a vertical line, m = Δy/Δx = undefined

Slope of Perpendicular Lines

A set of perpendicular lines always has 90º angle between them. Let us suppose we have two perpendicular lines l 1 and l 2 in the coordinate plane, inclined at angle θ 1 and θ 2 respectively with the x-axis, such that the given angles follow the external angle theorem as, θ 2 = θ 1 + 90º.

Therefore, their slopes can be given as, m 1 = tan θ 1 m 2 = tan (θ 1 + 90º) = - cot θ 1 ⇒ m 1 × m 2 = -1

Thus, the product of slopes of two perpendicular lines is equal to -1.

Slope of Parallel Lines

A set of parallel lines always have an equal angle of inclination. Let us suppose we have two parallel lines l 1 and l 2 in the coordinate plane, inclined at angle θ 1 and θ 2 respectively with the x-axis, such that the, θ 2 = θ 1 .

Therefore, their slopes can be given as, ⇒ m 1 = m 2

Thus, the slopes of the two parallel lines are equal.

Important Notes on Slope:

  • The slope of a line is the measure of the tangent of the angle made by the line with the x-axis.
  • The slope is constant throughout a straight line.
  • The slope-intercept form of a straight line can be given by y = mx + b
  • The slope is represented by the letter m, and is given by, m = tan θ = (y 2 - y 1 )/(x 2 - x 1 )

Challenging Question:

A line has the equation y = 2x - 7. Find the equation of a line that is perpendicular to the given line, and is passing through the origin.

☛ Related Topics:

  • Linear Equation
  • Quadratic Equation
  • Cubic Equation

Solved Examples on Slope

Example 1: Given a line with the equation, 2y = 8x + 9, find its slope.

We know that the general formula of the slope is given as, y = mx + b

Hence, we try to bring the equation to this form. We make the coefficient of y = 1, and hence we get,

y = 4x + 4.5

Clearly, the coefficient of x is found to be 4. Hence, our slope will be same as the coefficient of x .

The slope is 4.

Example 2: The equation of a line is given as x = 5. Find the slope of the given line.

The equation is given as x = 5. We can thus see that y is missing from our equation. Hence, we can assume the coefficient of y to be 0 for now. Thus we now get,

(0)y = x - 5

Now, we try to make the coefficient of y as 1. Let us try dividing both sides by Zero. We know that mathematically, if any real is divided by Zero, then the value can not be determined.

In this case, the coefficient of x divided by Zero will give us our slope. But we know that the answer will not be defined in such a case. So we can safely say that our slope is not defined in such cases.

Slope is not defined.

Example 3: If the rise is 10 units, while the run is just 5 units, find the slope of the line.

We know that the slope of a line will be

m = Rise/Run

Now, substituting the values, we will get

m = Rise/Run = 10/5 = 2

Slope is 2.

Example 4: Find the slope of a line that is parallel to the x-axis and intersects the y - axis at y = 4.

We know that the slope of any line is the tangent of its angle made with the x-axis. So, if the line is given to be parallel to the x-axis itself, then the angle made will be 0º. Hence, tan 0º will be 0. So the value of the slope is found to be,

m = tan 0 = 0

Hence, the value of the slope will be Zero.

Slope is 0.

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geometry assignment find the slope of each line

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Practice Questions on Slope

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FAQs on Slope

What is the slope of a line.

The slope of a line, also known as the gradient is defined as the value of the steepness or the direction of a line in a coordinate plane. Slope can be calculated using different methods, given the equation of a line or the coordinates of points lying on the straight line.

What is the Formula to Find Slope of a Line?

We can calculate the slope of a line directly using the slope of a line formula given the coordinates of the two points lying on the line. The formula is given as, Slope = m = tan θ = (y 2 - y 1 )/(x 2 - x 1 )

How to Calculate the Slope?

The slope is found by measuring the tangent of the angle made by the line with the x-axis. There are different methods to find the slope of a line. The expression that can be used to find the slope is given as tan θ or (y 2 - y 1 )/(x 2 - x 1 ), where θ is the angle which the line makes with the positive x-axis and (x 1 , y 1 ) and (x 2 , y 2 ) are the coordinates of the two points lying on the line.

What are the 4 Different Types of Slopes?

The 4 different types of slopes are positive slope, negative slope, zero slope, and undefined slope .

What is an Undefined Slope?

Any slope that has an angle of 90º with the x-axis, will have an undefined value of the tangent of 90º. Hence, such lines will have an undefined value of the slope.

What Does Slope Look Like?

The slope is nothing but the measure of the tangent of the angle made with the x-axis. Hence, it is just the measure of an angle.

What are 3 Ways to Find Slope?

The ways to find slope are point slope form , slope-intercept form , and the standard form. We can apply any of the forms of the equation of a straight line given the required information to find the slope.

How do you Show that Three Points are Collinear by Slope?

To prove the collinearity of three points, say A, B, and C, we can apply the slope formula. The slope of lines AB and BC should be equal for the three given points to be collinear points .

How to Find Slope With Two Points?

The slope can be calculated using the coordinates of two points using the formula, m = (y 2 - y 1 )/(x 2 - x 1 ), where (x 1 , y 1 ) and (x 2 , y 2 ) are the coordinates of the two points lying on the line.

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Course: Algebra 1   >   Unit 5

Intro to slope-intercept form.

  • Slope and y-intercept from equation
  • Worked examples: slope-intercept intro
  • Slope-intercept intro
  • Linear equation word problems
  • Linear equations word problems

What you should be familiar with before taking this lesson

  • You should know what two-variable linear equations are. Specifically, you should know that the graph of such equations is a line. If this is new to you, check out our intro to two-variable equations .
  • You should also be familiar with the following properties of linear equations: y ‍   -intercept and x ‍   -intercept and slope .

What you will learn in this lesson

  • What is the slope-intercept form of two-variable linear equations
  • How to find the slope and the y ‍   -intercept of a line from its slope-intercept equation
  • How to find the equation of a line given its slope and y ‍   -intercept

What is slope-intercept form?

  • y = 2 x + 1 ‍  
  • y = − 3 x + 2.7 ‍  
  • y = 10 − 100 x ‍   [But this equation has x in the last term!]
  • 2 x + 3 y = 5 ‍  
  • y − 3 = 2 ( x − 1 ) ‍  
  • x = 4 y − 7 ‍  

The coefficients in slope-intercept form

  • The slope is m ‍   .
  • The y ‍   -coordinate of the y ‍   -intercept is b ‍   . In other words, the line's y ‍   -intercept is at ( 0 , b ) ‍   .

Check your understanding

  • Your answer should be
  • an integer, like 6 ‍  
  • a simplified proper fraction, like 3 / 5 ‍  
  • a simplified improper fraction, like 7 / 4 ‍  
  • a mixed number, like 1   3 / 4 ‍  
  • an exact decimal, like 0.75 ‍  
  • a multiple of pi, like 12   pi ‍   or 2 / 3   pi ‍  
  • (Choice A)   ( 0 , − 6 ) ‍   A ( 0 , − 6 ) ‍  
  • (Choice B)   ( 0 , − 11 ) ‍   B ( 0 , − 11 ) ‍  
  • (Choice C)   ( − 6 , 0 ) ‍   C ( − 6 , 0 ) ‍  
  • (Choice D)   ( − 11 , 0 ) ‍   D ( − 11 , 0 ) ‍  
  • (Choice A)   ( 0 , 0 ) ‍   A ( 0 , 0 ) ‍  
  • (Choice B)   ( 0 , 1 4 ) ‍   B ( 0 , 1 4 ) ‍  
  • (Choice C)   ( 0 , 4 ) ‍   C ( 0 , 4 ) ‍  
  • (Choice D)   ( 0 , − 4 ) ‍   D ( 0 , − 4 ) ‍  
  • (Choice A)   y = − 3 x + 4 ‍   A y = − 3 x + 4 ‍  
  • (Choice B)   y = 4 x + 7 ‍   B y = 4 x + 7 ‍  
  • (Choice C)   y = 5 + 4 x ‍   C y = 5 + 4 x ‍  
  • (Choice D)   y = 4 − x ‍   D y = 4 − x ‍  
  • (Choice A)   The slope is the first number that appears in the equation. A The slope is the first number that appears in the equation.
  • (Choice B)   The slope is the coefficient of x ‍   , regardless of order. B The slope is the coefficient of x ‍   , regardless of order.
  • (Choice A)   y = 2 x + 3 ‍   A y = 2 x + 3 ‍  
  • (Choice B)   y = 2 x − 3 ‍   B y = 2 x − 3 ‍  
  • (Choice C)   y = − 2 x + 3 ‍   C y = − 2 x + 3 ‍  
  • (Choice D)   y = − 2 x − 3 ‍   D y = − 2 x − 3 ‍  

Why does this work?

Why b ‍   gives the y ‍   -intercept, why m ‍   gives the slope, want to join the conversation.

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Incredible Answer

Slope Calculator

How to use this slope calculator, the slope formula, how to find slope, other related topics, making this slope calculator.

The slope calculator determines the slope or gradient between two points in the Cartesian coordinate system. The slope is basically the amount of slant a line has and can have a positive, negative, zero, or undefined value. Before using the calculator, it is probably worth learning how to find the slope using the slope formula. To find the equation of a line for any given two points that this line passes through, use our slope intercept form calculator .

Here, we will walk you through how to use this calculator, along with an example calculation, to make it simpler for you. To calculate the slope of a line, you need to know any two points on it:

Enter the x and y coordinates of the first point on the line.

Enter the x and y coordinates of the second point on the line.

We instantly get the slope of the line . But the magic doesn't stop there, for you also get a bunch of extra results for good measure:

  • The equation of your function (same as the equation of the line).
  • The y-intercept of the line.
  • The angle the line makes with respect to the x-axis (measure anti-clockwise).
  • Slope as a percentage (percentage grade).
  • The distance between the two points.

For example , say you have a line that passes through the points (1, 5) and (7, 6) . Enter the x and y coordinates of the first point, followed by the x and y coordinates of the second one. Instantly, we learn that the line's slope is 0.166667 . If we need the line's equation, we also have it now: y = 0.16667x + 4.83333 .

You can use this calculator in reverse and find a missing x or y coordinate! For example, consider the line that passes through the point (9, 12) and has a 12% slope. To find the point where the line crosses the y-axis (i.e., x = 0 ), enter 12% in percent grade (9, 12) as the coordinate of the first point, and x 2 = 0 . Right away, the calculator tells us that y 2 = 10.92 .

The slope of a line has many significant uses in geometry and calculus. The article below is an excellent introduction to the fundamentals of this topic, and we insist that you give it a read.

Notice that the slope of a line is easily calculated by hand using small, whole number coordinates. The formula becomes increasingly useful as the coordinates take on larger values or decimal values.

It is worth mentioning that any horizontal line has a gradient of zero because a horizontal line has the same y-coordinates. This will result in a zero in the numerator of the slope formula. On the other hand, a vertical line will have an undefined slope since the x-coordinates will always be the same. This will result the division by zero error when using the formula.

Identify the coordinates ( x 1 , y 1 ) (x_1, y_1) ( x 1 ​ , y 1 ​ ) and ( x 2 , y 2 ) (x_2, y_2) ( x 2 ​ , y 2 ​ ) . We will use the formula to calculate the slope of the line passing through the points ( 3 , 8 ) (3, 8) ( 3 , 8 ) and ( − 2 , 10 ) (-2, 10) ( − 2 , 10 ) .

Input the values into the formula. This gives us ( 10 − 8 ) / ( − 2 − 3 ) (10 - 8)/(-2 - 3) ( 10 − 8 ) / ( − 2 − 3 ) .

Subtract the values in parentheses to get 2 / ( − 5 ) 2/(-5) 2/ ( − 5 ) .

Simplify the fraction to get the slope of − 2 / 5 -2/5 − 2/5 .

Check your result using the slope calculator.

To find the slope of a line, we need two coordinates on the line. Any two coordinates will suffice. We are basically measuring the amount of change of the y-coordinate, often known as the rise , divided by the change of the x-coordinate, known as the run . The calculations in finding the slope are simple and involve nothing more than basic subtraction and division.

🙋 To find the gradient of non-linear functions, you can use the average rate of change calculator .

Just as slope can be calculated using the endpoints of a segment, the midpoint can also be calculated. The midpoint is an important concept in geometry, particularly when inscribing a polygon inside another polygon with its vertices touching the midpoint of the sides of the larger polygon. This can be obtained using the midpoint calculator or by simply taking the average of each x-coordinates and the average of the y-coordinates to form a new coordinate.

The slopes of lines are important in determining whether or not a triangle is a right triangle. If any two sides of a triangle have slopes that multiply to equal -1, then the triangle is a right triangle. The computations for this can be done by hand or by using the right triangle calculator . You can also use the distance calculator to compute which side of a triangle is the longest, which helps determine which sides must form a right angle if the triangle is right.

The sign in front of the gradient provided by the slope calculator indicates whether the line is increasing, decreasing, constant or undefined. If the graph of the line moves from lower left to upper right it is increasing and is therefore positive. If it decreases when moving from the upper left to lower right, then the gradient is negative.

The slope calculator is one of the oldest at Omni Calculator, built by our veterans Mateusz and Julia, who make creating accurate scientific tools look easy. The idea for this calculator was born when the two were crunching data analytics and trends and realized how a slope calculator would make their job easier. Even today, you can find them occasionally using this tool for reliable calculations.

We put extra care into the quality of our content so that it is as accurate and dependable as possible. Each tool is peer-reviewed by a trained expert and then proofread by a native speaker. You can learn more about our standards in our Editorial Policies page.

How to find slope from an equation?

The method for finding the slope from an equation will vary depending on the form of the equation in front of you. If the form of the equation is y = mx + c, then the slope (or gradient) is just m . If the equation is not in this form, try to rearrange the equation. To find the gradient of other polynomials, you will need to differentiate the function with respect to x .

How do you calculate the slope of a hill?

Use a map to determine the distance between the top and bottom of the hill as the crow flies.

Using the same map, or GPS, find the altitude between the top and bottom of the hill . Make sure that the points you measure from are the same as step 1.

Convert both measurements into the same units.

Divide the difference in altitude by the distance between the two points.

This number is the gradient of the hill if it increases linearly. If it does not, repeat the steps but at where there is a noticeable change in slope.

How do you calculate the length of a slope?

Measure the difference between the top and bottom of the slope in relation to both the x and y axis.

If you can only measure the change in x, multiply this value by the gradient to find the change in the y axis.

Make sure the units for both values are the same.

Use the Pythagorean theorem to find the length of the slope . Square both the change in x and the change in y.

Add the two values together.

Find the square root of the summation.

This new value is the length of the slope.

What is a 1 in 20 slope?

A 1/20 slope is one that rises by 1 unit for every 20 units traversed horizontally . So, for example, a ramp that was 200 ft long and 10 ft tall would have a 1/20 slope. A 1/20 slope is equivalent to a gradient of 1/20 (strangely enough) and forms an angle of 2.86° between itself and the x-axis.

How do you find the slope of a curve?

As the slope of a curve changes at each point, you can find the slope of a curve by differentiating the equation with respect to x and, in the resulting equation, substituting x for the point at which you’d like to find the gradient.

Is rate of change the same as slope?

The rate of change of a graph is also its slope , which are also the same as gradient. Rate of change can be found by dividing the change in the y (vertical) direction by the change in the x (horizontal) direction, if both numbers are in the same units, of course. Rate of change is particularly useful if you want to predict the future of previous value of something , as, by changing the x variable, the corresponding y value will be present (and vice versa).

Where do you use slope in everyday life?

Slopes (or gradients) have a number of uses in everyday life . There are some obvious physical examples - every hill has a slope, and the steeper the hill, the greater its gradient . This can be useful if you are looking at a map and want to find the best hill to cycle down. You also probably sleep under a slope, a roof that is . The slope of a roof will change depending on the style and where you live. But, more importantly, if you ever want to know how something changes with time, you will end up plotting a graph with a slope .

What is a 10% slope?

A 10% slope is one that rises by 1 unit for every 10 units travelled horizontally (10 %). For example, a roof with a 10% slope that is 20 m across will be 2 m high. This is the same as a gradient of 1/10 , and an angle of 5.71° is formed between the line and the x-axis.

How do you find the area under a slope?

To find the area under a slope given by the equation y = mx + c, follow these steps:

  • Define the lower and upper bounds of x to get a value for Δx.
  • Multiply Δx by the slope (m) to obtain Δy.
  • Multiply Δx by Δy.
  • Divide by 2 to give you the area under the slope.

What degree is a 1 to 5 slope?

A 1 to 5 slope is one that, for every increase of 5 units horizontally, rises by 1 unit . The number of degrees between a 1 to 5 slope and the x-axis is 11.3°. This can be found by first calculating the slope, by dividing the change in the y direction by the change in the x direction, and then finding the inverse tangent of the slope.

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Module 8QR: Modeling Growth

Slope of a line, learning outcomes.

  • Identify rise and run from a graph

Distinguish between graphs of lines with negative and positive slopes

  • Use the formula for slope to define the slope of a line through two points
  • Find the slope of the lines [latex]x=a[/latex] and [latex]y=b[/latex]
  • Recognize that horizontal lines have slope = 0
  • Recognize that vertical lines have slopes that are undefined
  • Given a line, identify the slope of another line that is parallel to it
  • Given a line, identify the slope of another line that is perpendicular to it
  • Verify the slope of a linear equation given a dataset
  • Interpret the slope of a linear equation as it applies to a real situation

Identify slope from a graph

The mathematical definition of slope is very similar to our everyday one. In math, slope is used to describe the steepness and direction of lines. By just looking at the graph of a line, you can learn some things about its slope, especially relative to other lines graphed on the same coordinate plane. Consider the graphs of the three lines shown below:

Three different lines on a graph. Line A is tilted upward. Line B is sharply titled upward. Line C is sharply tilted downward.

First, let’s look at lines A and B. If you imagined these lines to be hills, you would say that line B is steeper than line A. Line B has a greater slope than line A.

Next, notice that lines A and B slant up as you move from left to right. We say these two lines have a positive slope. Line C slants down from left to right. Line C has a negative slope. Using two of the points on the line, you can find the slope of the line by finding the rise and the run. The vertical change between two points is called the rise , and the horizontal change is called the run . The slope equals the rise divided by the run: [latex] \displaystyle \text{Slope }=\frac{\text{rise}}{\text{run}}[/latex].

A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.

You can determine the slope of a line from its graph by looking at the rise and run. One characteristic of a line is that its slope is constant all the way along it. So, you can choose any 2 points along the graph of the line to figure out the slope. Let’s look at an example.

Use the graph to find the slope of the line.

A line that crosses the points (2,1) and (6,3). A blue line labeled Rise goes up two units from the point (2,1). A red line labeled Run goes left from the point (6,3) so that it forms a triangle with the main line and the Rise line. A formula says slope equals rise over run.

[latex]\frac{1}{2}[/latex]

This line will have a slope of [latex] \displaystyle \frac{1}{2}[/latex] no matter which two points you pick on the line. Try measuring the slope from the origin, [latex](0,0)[/latex], to the point [latex](6,3)[/latex]. You will find that the [latex]\text{rise}=3[/latex] and the [latex]\text{run}=6[/latex]. The slope is [latex] \displaystyle \frac{\text{rise}}{\text{run}}=\frac{3}{6}=\frac{1}{2}[/latex]. It is the same!

Let’s look at another example.

Use the graph to find the slope of the two lines.  

A graph showing two lines with their rise and run. The first line is drawn through the points (-2,1) and (-1,5). The rise goes up from the point (-2,1) to join with the run line that goes right to the point (-1,5). The second line is drawn through the points (-1,-2) and (3,-1). The rise goes up from the point (-1,-2) to join with the run to go right to the point (3,-1).

The slope of the blue line is 4 and the slope of the red line is [latex]\frac{1}{4}[/latex].

When you look at the two lines, you can see that the blue line is steeper than the red line. It makes sense the value of the slope of the blue line, 4, is greater than the value of the slope of the red line, [latex] \displaystyle \frac{1}{4}[/latex]. The greater the slope, the steeper the line.

Finding the Slope of a Line From a Graph

Direction is important when it comes to determining slope. It’s important to pay attention to whether you are moving up, down, left, or right; that is, if you are moving in a positive or negative direction. If you go up to get to your second point, the rise is positive. If you go down to get to your second point, the rise is negative. If you go right to get to your second point, the run is positive. If you go left to get to your second point, the run is negative.

In the following two examples, you will see a slope that is positive and one that is negative.

Example (Advanced)

Find the slope of the line graphed below.

Line drawn through the point (-3,-0.25) and (3,4.25).

The slope of the line is 0.75.

The next example shows a line with a negative slope.

A downward-sloping line that goes through points A and B. Point A is (0,4) and point B is (2,1). The rise goes down three units, and the run goes right 2 units.

The slope of the line is [latex]-\frac{3}{2}[/latex].

In the example above, you could have found the slope by starting at point B, running [latex]{-2}[/latex], and then rising [latex]+3[/latex] to arrive at point A. The result is still a slope of [latex]\displaystyle\frac{\text{rise}}{\text{run}}=\frac{+3}{-2}=-\frac{3}{2}[/latex].

Finding the Slope from Two Points on the Line

You’ve seen that you can find the slope of a line on a graph by measuring the rise and the run. You can also find the slope of a straight line without its graph if you know the coordinates of any two points on that line. Every point has a set of coordinates: an x -value and a y -value, written as an ordered pair ( x , y ). The x value tells you where a point is horizontally. The y value tells you where the point is vertically.

Consider two points on a line—Point 1 and Point 2. Point 1 has coordinates [latex]\left(x_{1},y_{1}\right)[/latex] and Point 2 has coordinates [latex]\left(x_{2},y_{2}\right)[/latex].

A line with its rise and run. The first point on the line is labeled Point 1, or (x1, y1). The second point on the line is labeled Point 2, or (x2,y2). The rise is (y2 minus y1). The run is (x2 minus X1).

The rise is the vertical distance between the two points, which is the difference between their y -coordinates. That makes the rise [latex]\left(y_{2}-y_{1}\right)[/latex]. The run between these two points is the difference in the x -coordinates, or [latex]\left(x_{2}-x_{1}\right)[/latex].

So, [latex] \displaystyle \text{Slope}=\frac{\text{rise}}{\text{run}}[/latex] or [latex] \displaystyle m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}[/latex]

In the example below, you’ll see that the line has two points each indicated as an ordered pair. The point [latex](0,2)[/latex] is indicated as Point 1, and [latex](−2,6)[/latex] as Point 2. So you are going to move from Point 1 to Point 2. A triangle is drawn in above the line to help illustrate the rise and run.

A line going through Point 1, or (0,2), and Point 2, or (-2,6). The rise is 4 and the run is -2.

You can see from the graph that the rise going from Point 1 to Point 2 is 4, because you are moving 4 units in a positive direction (up). The run is [latex]−2[/latex], because you are then moving in a negative direction (left) 2 units. Using the slope formula,

[latex] \displaystyle \text{Slope}=\frac{\text{rise}}{\text{run}}=\frac{4}{-2}=-2[/latex].

You do not need the graph to find the slope. You can just use the coordinates, keeping careful track of which is Point 1 and which is Point 2. Let’s organize the information about the two points:

The slope, [latex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{6-2}{-2-0}=\frac{4}{-2}=-2[/latex]. The slope of the line, m , is [latex]−2[/latex].

It doesn’t matter which point is designated as Point 1 and which is Point 2. You could have called [latex](−2,6)[/latex] Point 1, and [latex](0,2)[/latex] Point 2. In that case, putting the coordinates into the slope formula produces the equation [latex]m=\frac{2-6}{0-\left(-2\right)}=\frac{-4}{2}=-2[/latex]. Once again, the slope is [latex]m=-2[/latex]. That’s the same slope as before. The important thing is to be consistent when you subtract: you must always subtract in the same order [latex]\left(y_{2},y_{1}\right)[/latex]   and [latex]\left(x_{2},x_{1}\right)[/latex].

What is the slope of the line that contains the points [latex](5,5)[/latex] and [latex](4,2)[/latex]?

The slope is 3.

The example below shows the solution when you reverse the order of the points, calling [latex](5,5)[/latex] Point 1 and [latex](4,2)[/latex] Point 2.

Notice that regardless of which ordered pair is named Point 1 and which is named Point 2, the slope is still 3.

What is the slope of the line that contains the points [latex](3,-6.25)[/latex] and [latex](-1,8.5)[/latex]?

The slope is [latex]-3.6875[/latex].

Let’s consider a horizontal line on a graph. No matter which two points you choose on the line, they will always have the same y -coordinate. The equation for this line is [latex]y=3[/latex]. The equation can also be written as [latex]y=\left(0\right)x+3[/latex].

Video: Finding the Slope of a Line Given Two Points on the Line

Finding the Slopes of Horizontal and Vertical Lines

So far you’ve considered lines that run “uphill” or “downhill.” Their slopes may be steep or gradual, but they are always positive or negative numbers. But there are two other kinds of lines, horizontal and vertical. What is the slope of a flat line or level ground? Of a wall or a vertical line?

The line y=3 crosses through the point (-3,3); the point (0,3); the point (2,3); and the point (5,3).

Using the form [latex]y=0x+3[/latex], you can see that the slope is 0. You can also use the slope formula with two points on this horizontal line to calculate the slope of this horizontal line. Using [latex](−3,3)[/latex] as Point 1 and (2, 3) as Point 2, you get:

[latex] \displaystyle \begin{array}{l}m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\\\\m=\frac{3-3}{2-\left(-3\right)}=\frac{0}{5}=0\end{array}[/latex]

The slope of this horizontal line is 0.

Let’s consider any horizontal line. No matter which two points you choose on the line, they will always have the same y -coordinate. So, when you apply the slope formula, the numerator will always be 0. Zero divided by any non-zero number is 0, so the slope of any horizontal line is always 0.

The equation for the horizontal line [latex]y=3[/latex] is telling you that no matter which two points you choose on this line, the y- coordinate will always be 3.

How about vertical lines? In their case, no matter which two points you choose, they will always have the same x -coordinate. The equation for this line is [latex]x=2[/latex].

The line x=2 runs through the point (2,-2), the point (2,1), the point (2,3), and the point (2,4).

There is no way that this equation can be put in the slope-point form, as the coefficient of y is [latex]0\left(x=0y+2\right)[/latex].

So, what happens when you use the slope formula with two points on this vertical line to calculate the slope? Using [latex](2,1)[/latex] as Point 1 and [latex](2,3)[/latex] as Point 2, you get:

[latex] \displaystyle \begin{array}{l}m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}\\\\m=\frac{3-1}{2-2}=\frac{2}{0}\end{array}[/latex]

But division by zero has no meaning for the set of real numbers. Because of this fact, it is said that the slope of this vertical line is undefined. This is true for all vertical lines—they all have a slope that is undefined.

What is the slope of the line that contains the points [latex](3,2)[/latex] and [latex](−8,2)[/latex]?

The slope is 0, so the line is horizontal.

Finding Slopes of Horizontal and Vertical Lines

Characterize the slopes of parallel and perpendicular lines

When you graph two or more linear equations in a coordinate plane, they generally cross at a point. However, when two lines in a coordinate plane never cross, they are called parallel lines . You will also look at the case where two lines in a coordinate plane cross at a right angle. These are called perpendicular lines . The slopes of the graphs in each of these cases have a special relationship to each other.

Parallel lines are two or more lines in a plane that never intersect. Examples of parallel lines are all around us, such as the opposite sides of a rectangular picture frame and the shelves of a bookcase.

Line y=2x+3 and line y=2x-3. Caption says Equations of parallel lines will have the same slopes and different intercepts.

Perpendicular lines are two or more lines that intersect at a 90-degree angle, like the two lines drawn on this graph. These 90-degree angles are also known as right angles.

Two lines that cross to form a 90 degree angle.

Perpendicular lines are also everywhere, not just on graph paper but also in the world around us, from the crossing pattern of roads at an intersection to the colored lines of a plaid shirt.

Parallel Lines

Two non-vertical lines in a plane are parallel if they have both:

  • the same slope
  • different y -intercepts

Any two vertical lines in a plane are parallel.

Find the slope of a line parallel to the line [latex]y=−3x+4[/latex].

Identify the slope of the given line.

The given line is written in [latex]y=mx+b[/latex] form, with [latex]m=−3[/latex] and [latex]b=4[/latex]. The slope is [latex]−3[/latex].

A line parallel to the given line has the same slope.

The slope of the parallel line is [latex]−3[/latex].

Determine whether the lines [latex]y=6x+5[/latex] and [latex]y=6x–1[/latex] are parallel.

Identify the slopes of the given lines.

The given lines are written in [latex]y=mx+b[/latex] form, with [latex]m=6[/latex] for the first line and [latex]m=6[/latex] for the second line. The slope of both lines is 6.

Look at b , the y -value of the y -intercept, to see if the lines are perhaps exactly the same line, in which case we don’t say they are parallel.

The first line has a y -intercept at [latex](0,5)[/latex], and the second line has a y -intercept at [latex](0,−1)[/latex]. They are not the same line.

The slopes of the lines are the same and they have different y -intercepts, so they are not the same line and they are parallel.

The lines are parallel.

Perpendicular Lines

Two non-vertical lines are perpendicular if the slope of one is the negative reciprocal of the slope of the other. If the slope of the first equation is 4, then the slope of the second equation will need to be [latex]-\frac{1}{4}[/latex] for the lines to be perpendicular.

You can also check the two slopes to see if the lines are perpendicular by multiplying the two slopes together. If they are perpendicular, the product of the slopes will be [latex]−1[/latex]. For example, [latex] 4\cdot-\frac{1}{4}=\frac{4}{1}\cdot-\frac{1}{4}=-1[/latex].

Find the slope of a line perpendicular to the line [latex]y=2x–6[/latex].

The slope of the perpendicular line is [latex]-\tfrac{1}{2}[/latex].

To find the slope of a perpendicular line, find the reciprocal, [latex] \displaystyle \tfrac{1}{2}[/latex], and then find the opposite of this reciprocal [latex] \displaystyle -\tfrac{1}{2}[/latex].

Note that the product [latex]2\left(-\frac{1}{2}\right)=\frac{2}{1}\left(-\frac{1}{2}\right)=-1[/latex], so this means the slopes are perpendicular.

In the case where one of the lines is vertical, the slope of that line is undefined and it is not possible to calculate the product with an undefined number. When one line is vertical, the line perpendicular to it will be horizontal, having a slope of zero ([latex]m=0[/latex]).

Determine whether the lines [latex]y=−8x+5[/latex] and [latex] \displaystyle y\,\text{=}\,\,\frac{1}{8}x-1[/latex] are parallel, perpendicular, or neither.

The given lines are written in [latex]y=mx+b[/latex] form, with [latex]m=−8[/latex] for the first line and [latex]m=\frac{1}{8}[/latex] for the second line.

Determine if the slopes are the same or if they are opposite reciprocals.

[latex]-8\ne\frac{1}{8}[/latex], so the lines are not parallel.

The opposite reciprocal of [latex]−8[/latex] is [latex] \displaystyle \frac{1}{8}[/latex], so the lines are perpendicular.

The slopes of the lines are opposite reciprocals, so the lines are perpendicular.

The lines are perpendicular.

The Slope of Parallel and Perpendicular Lines

Verify Slope From a Dataset

Massive amounts of data is being collected every day by a wide range of institutions and groups.  This data is used for many purposes including business decisions about location and marketing, government decisions about allocation of resources and infrastructure, and personal decisions about where to live or where to buy food.

In the following example, you will see how a dataset can be used to define the slope of a linear equation.

Given the dataset, verify the values of the slopes of each equation.

Linear equations describing the change in median home values between 1950 and 2000 in Mississippi and Hawaii are as follows:

Hawaii:  [latex]y=3966x+74,400[/latex]

Mississippi:   [latex]y=924x+25,200[/latex]

The equations are based on the following dataset.

x = the number of years since 1950, and y = the median value of a house in the given state.

The slopes of each equation can be calculated with the formula you learned in the section on slope.

[latex] \displaystyle m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}[/latex]

Mississippi:

[latex] \displaystyle m=\frac{{71,400}-{25,200}}{{50}-{0}}=\frac{{46,200}}{{50}} = 924[/latex]

We have verified that the slope [latex] \displaystyle m = 924[/latex] matches the dataset provided.

[latex]\displaystyle m=\frac{{272,700}-{74,400}}{{50}-{0}}=\frac{{198,300}}{{50}} = 3966[/latex]

We have verified that the slope [latex] \displaystyle m = 3966[/latex] matches the dataset provided.

Given the dataset, verify the values of the slopes of the equation.

A linear equation describing the change in the number of high school students who smoke, in a group of 100, between 2011 and 2015 is given as:

 [latex]y = -1.75x+16[/latex]

And is based on the data from this table, provided by the Centers for Disease Control.

x = the number of years since 2011, and y = the number of high school smokers per 100 students.

[latex] \displaystyle m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}=\frac{{9-16}}{{4-0}} =\frac{{-7}}{{4}}=-1.75[/latex]

We have verified that the slope [latex] \displaystyle{m=-1.75}[/latex] matches the dataset provided.

Interpret the Slope of  Linear Equation

Okay, now we have verified that data can provide us with the slope of a linear equation. So what? We can use this information to describe how something changes using words.

First, let’s review the different kinds of slopes possible in a linear equation.

We often use specific words to describe the different types of slopes when we are using lines and equations to represent “real” situations. The following table pairs the type of slope with the common language used to describe it both verbally and visually.

Interpret the slope of each equation for house values using words.

Hawaii:  [latex]y = 3966x+74,400[/latex]

Mississippi:   [latex]y = 924x+25,200[/latex]

For Mississippi:

[latex] \displaystyle m=\frac{{71,400}-{25,200}}{{0}-{50}}=\frac{{46,200\text{ dollars}}}{{50\text{ year}}} = 924\frac{\text{dollars}}{\text{year}}[/latex]

The slope for the Mississippi home prices equation is positive , so each year the price of a home in Mississippi  increases by 924 dollars.

We can apply the same thinking for Hawaii home prices. The slope for the Hawaii home prices equation tells us that each year, the price of a home increases by 3966 dollars.

Interpret the Meaning of the Slope Given a Linear Equation—Median Home Values

Interpret the slope of the line describing the change in the number of high school smokers using words.

Apply units to the formula for slope. The x values represent years, and the y values represent the number of smokers. Remember that this dataset is per 100 high school students.

[latex] \displaystyle m=\frac{{9-16}}{{2015-2011}} =\frac{{-7 \text{ smokers}}}{{4\text{ year}}}=-1.75\frac{\text{ smokers}}{\text{ year}}[/latex]

The slope of this linear equation is negative , so this tells us that there is a decrease in the number of high school age smokers each year.

The number of high schoolers that smoke decreases by 1.75 per 100 each year.

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  • Slope Of Line

Slope of a Line

In geometry, we have seen the lines drawn on the coordinate plane. To predict whether the lines are parallel or perpendicular or at any angle without using any geometrical tool, the best way to find this is by measuring the slope. In this article, we are going to discuss what a slope is, slope formula for parallel lines , perpendicular lines, slope for collinearity with many solved examples in detail.

What is a Slope?

In Mathematics, a slope of a line is the change in y coordinate with respect to the change in x coordinate.

The net change in y-coordinate is represented by Δy and the net change in x-coordinate is represented by Δx.

Hence, the change in y-coordinate with respect to the change in x-coordinate is given by,

m = change in y/change in x = Δy/Δx

Where “m” is the slope of a line.

The slope of the line can also be represented by

tan θ = Δy/Δx

So, tan θ to be the slope of a line.

Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x 1 ,y 1 ) and (x 2 ,y 2 ) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ‘m’. 

Slope Formula

If P(x 1 ,y 1 ) and Q(x 2 ,y 2 ) are the two points on a straight line, then the slope formula is given by:

Therefore, based on the above formula, we can easily calculate the slope of a line between two points. 

In other term, the slope of a line between two points is also said to be the rise of the line from one point to another (along y-axis) over the run (along x-axis). Therefore, 

Slope, m = Rise/Run

Slope of a Line Equation

The equation for the slope of a line and the points also called point slope form of equation of a straight line is given by:

Whereas the slope-intercept form the equation of the line is given by:

Where b is the y-intercept.

How to Find Slope of a Line on a Graph?

In the given figure, if the angle of inclination of the given line with the x-axis is θ then, the slope of the line is given by tan θ. Hence, there is a relation between the lines and angles . In this article, you will learn various formulas related to the angles and lines.

Slope of a line

The slope of a line is given as m = tan θ. If two points A (x 1 , y 1) and B(x 2 , y 2 ) lie on the line with x 1 ≠ x 2  then the slope of the line AB is given as:

\(\begin{array}{l} m = tan\ \theta =\frac{y_2~-~y_1}{x_2~-~x_1}\end{array} \)

Where θ is the angle which the line AB makes with the positive direction of the x-axis. θ lies between 0° and 180°.

It must be noted that θ = 90° is only possible when the line is parallel to y-axis i.e. at x 1 = x 2  at this particular angle the slope of the line is undefined.

Conditions for perpendicularity, parallelism, and collinearity of straight lines are given below:

Slope for Parallel Lines

Consider two parallel lines given by l 1 and l 2  with inclinations α and β respectively. For two lines to be parallel their inclination must also be equal i.e. α=β. This results in the fact that tan α = tan β. Hence, the condition for two lines with inclinations α, β to be parallel is tan α = tan β.

Slope of a line 2

Therefore, if the slopes of two lines on the Cartesian plane are equal, then the lines are parallel to each other.

Thus, if two lines are parallel then, m 1 = m 2 .

Generalizing this for n lines, they are parallel only when the slopes of all the lines are equal.

If the equation of the two lines are given as ax + by + c = 0 and a’ x + b’ y + c’= 0, then they are parallel when ab’ = a’b. (How? You can arrive at this result if you find the slopes of each line and equate them.)

Slope for Perpendicular Lines

Slope of a line

In the figure, we have two lines l 1 and l 2  with inclinations α, β. If they are perpendicular, we can say that β = α + 90°. (Using properties of angles)

Their slopes can be given as:

m 1 = tan(α + 90°) and m 2 = tan α.

Thus, for two lines to be perpendicular the product of their slope must be equal to -1.

If the equations of the two lines are given by ax + by + c = 0 and a’ x + b’ y + c’ = 0, then they are perpendicular if, aa’+ bb’ = 0. (Again, you can arrive at this result if you find the slopes of each line and equate their product to -1.)

Also, read: Perpendicular Lines

Slope for Collinearity

Slope of a line 3

For two lines AB and BC to be collinear the slope of both the lines must be equal and there should be at least one common point through which they should pass. Thus, for three points A, B, and C to be collinear the slopes of AB and BC must be equal.

If the equation of the two lines is given by ax + by + c = 0 and a’ x+b’ y+c’ = 0, then they are collinear when ab’ c’ = a’ b’ c = a’c’b.

Angle between Two Lines

Slope of a line 5

When two lines intersect at a point then the angle between them can be expressed in terms of their slopes and is given by the following formula:

where m 1 and m 2 are the slopes of the line AB and CD respectively.

Slope of Vertical Lines

Vertical lines have no slope, as they do not have any steepness. Or it can be said, we cannot define the steepness of vertical lines. 

A vertical line will have no values for x-coordinates. So, as per the formula of slope of the line, 

Slope, m = (y 2 – y 1 )/(x 2 – x 1 ) 

But for vertical lines, x 2 = x 1 = 0

m = (y 2 – y 1 )/0 = undefined

In the same way, the slope of horizontal line is equal to 0, since the y-coordinates are zero. 

m = 0/(x 2 – x 1 ) = 0 [for horizontal line]

Positive and Negative Slope

If the value of slope of a line is positive, it shows that line goes up as we move along or the rise over run is positive. 

If the value of slope is negative, then the line goes done in the graph as we move along the x-axis. 

Solved Examples on Slope of a Line

Find the slope of a line between the points P = (0, –1) and Q = (4,1).

Given,the points P = (0, –1) and Q = (4,1).

As per the slope formula we know that,

Slope of a line, m = (y 2 – y 1 )/(x 2 – x 1 ) 

m = (1-(-1))/(4-0) = 2/4 = ½

Find the slope of a line between P(–2, 3) and Q(0, –1).

Given,  P(–2, 3) and Q(0, –1) are the two points.

Therefore, slope of the line, 

m = (-1-3)/0-(-2) = -4/2 = -2

Ramya was checking the graph, and she realized that the raise was 10 units and the run was 5 units. What should be the the slope of a line?

Given that, Raise = 10 units

Run = 5 units.

We know that the slope of a line is defined as the ratio of raise to the run.

i.e. Slope, m = Raise/Run

Hence, slope = 10/5 = 2 units.

Therefore, the slope of a line is 2 units.

Frequently Asked Questions on Slope of a Line

What is the slope of a straight line, what are the three different ways to find the slope, what is the point-slope equation of a straight line, how to find slope of a line, what is the slope between two points, what is the slope of the line: y = −2x + 7.

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Algebra 1 Find The Slope Of Each Line

Algebra 1 Find The Slope Of Each Line - Displaying top 8 worksheets found for this concept.

Some of the worksheets for this concept are Algebra 1 section work find the slope of the line, Slope, Slope from a, Infinite algebra 1, Keystone exams algebra i, Assignment, Algebra 1 name per work for 1 equation options, The slope of a line.

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1. Algebra 1 Section 3.3 Worksheet Find the slope of the line ...

3. slope from a graph.ks-ia1, 4. infinite algebra 1, 5. keystone exams: algebra i, 6. assignment, 7. algebra 1 name: per: 2.1 worksheet for # 1 equation options, 8. the slope of a line.

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  1. Slope Worksheets

    Find the Slope: Ratio Method Use the x- and y- coordinates provided to find the slope (rise and run) of a line using the ratio method. A worked out example along with the formula is displayed at the top of each worksheet for easy reference. Download the set

  2. PDF Slope Date Period

    Find the slope of each line. 1) x y 2) x y 3) x y 4) x y 5) x y 6) x y 7) x y 8) x y-1-©B W2R0 f1K21 fK Su gtpa y 1S zo QfRtlw ja jr Ee4 lLyLSC2.c x QAPl 7ly Trpifg uh Tt3ss zr QeTsLe4r Xvle 6dq. c S PMZaAd Xe4 ywKiJt 5h o oI 7nWf0i ynri wtceO WP1r YeD-DA 4l Vg4e8bhr Zad. W Worksheet by Kuta Software LLC

  3. How to Find the Slope of a Line: Easy Guide with Examples

    Q&A | Tips If you're taking algebra, finding the slope of a line is an important concept to understand. But there are multiple ways to find the slope, and your teacher may expect you to learn them all. Feeling a bit overwhelmed? Don't fret. This guide explains how to find the slope of a line using ( x, y) points from graphs.

  4. Slope Calculator

    Find the Equation of the Line: y = mx + b by solving for y using the Point Slope Equation. y − y1 = m(x − x1) y − 3 = − 12 5 (x − 2) y − 3 = − 12 5 x − ( − 12 5 × 2) y − 3 = − 12 5 x − − 24 5 y − 3 = − 12 5 x + 24 5 y = − 12 5 x + 24 5 + 3 y = − 12 5 x + 39 5 m = − 12 5 b = 39 5 In decimals: y = − 2.4x + 7.8 Standard Form of a Linear Equation

  5. How To Find The Slope Of A Line

    The slope of a line is a measure of how steep a straight line is. In the general equation of a line or slope intercept form of a line, y=m x+b, y = mx + b, the slope is denoted by the coefficient m. m. Imagine walking up a set of stairs. Each step has the same height and you can only take one step forward each time you move.

  6. Slope formula (equation for slope)

    Step 1: Identify the values of x 1 , x 2 , y 1 , and y 2 . x 1 = 2 y 1 = 1 x 2 = 4 y 2 = 7 [Explain] Step 2: Plug in these values to the slope formula to find the slope. Slope = y 2 − y 1 x 2 − x 1 = 7 − 1 4 − 2 = 6 2 = 3 Step 3: Gut check. Make sure this slope makes sense by thinking about the points on the coordinate plane.

  7. Slope

    Get Started Slope The slope of a line is the measure of the steepness and the direction of the line. Finding the slope of lines in a coordinate plane can help in predicting whether the lines are parallel, perpendicular, or none without actually using a compass. The slope of any line can be calculated using any two distinct points lying on the line.

  8. PDF Slope From a Graph.ks-ia1

    Find the slope of each line. 1) x y 2) x y 3) x y 4) x y 5) x y 6) x y 7) x y 8) x y-1-©r B2N0w1y2 D nK ru0thay gS SoYf1tPwLasr meq aL4L1Cs. i 2 bA NlblG Trti bgghFtCsd zr vevs se Pr wvreidp. f 9 ZMca sd0e R 2wHist 9hf 8Ian EfDitn 5ibtke c UAvlxg oeUb8r3a W o1 R.q Worksheet by Kuta Software LLC 9) x y 10) x y 11) x y 12) x y

  9. Intro to slope

    Intro to slope. Slope tells us how steep a line is. It's like measuring how quickly a hill goes up or down. We find the slope by seeing how much we go up or down (vertical change) for each step to the right (horizontal change). If a line goes up 2 steps for every 1 step to the right, its slope is 2.

  10. Slope-intercept form introduction

    The slope-intercept form of a linear equation is where one side contains just "y". So, it will look like: y = mx + b where "m" and "b" are numbers. This form of the equation is very useful. The coefficient of "x" (the "m" value) is the slope of the line. And, the constant (the "b" value) is the y-intercept at (0, b)

  11. Slope Calculator

    FAQ The slope calculator determines the slope or gradient between two points in the Cartesian coordinate system. The slope is basically the amount of slant a line has and can have a positive, negative, zero, or undefined value. Before using the calculator, it is probably worth learning how to find the slope using the slope formula.

  12. Slope of a Line

    Use the formula for slope to define the slope of a line through two points. Find the Slope of Horizontal and Vertical Lines. Find the slope of the lines [latex]x=a [/latex] and [latex]y=b [/latex] Recognize that horizontal lines have slope = 0. Recognize that vertical lines have slopes that are undefined.

  13. Slope Calculator

    Free slope calculator - find the slope of a line given two points, a function or the intercept step-by-step

  14. Slope of a Line

    tan θ = Δy/Δx. So, tan θ to be the slope of a line. Generally, the slope of a line gives the measure of its steepness and direction. The slope of a straight line between two points says (x1,y1) and (x2,y2) can be easily determined by finding the difference between the coordinates of the points. The slope is usually represented by the letter ...

  15. PDF Infinite Algebra 1

    Find the slope of each line. 1) y 2) y x x Find the slope of the line through each pair of points. 3) (2, -10), (8, -16) 4) (-17, -5), (15, -13) Find the slope of each line. 9 5) y = x + 5 5 6) y = 5 Find the slope of a line parallel to each given line. 5 7) y = - x - 2 2 8) y = -x - 5

  16. Slopes of Parallel and Perpendicular Lines

    Line 2: Parallel Lines: The lines are parallel if their slopes are equal or the same. That means. Equal Slopes: Graph: Perpendicular Lines: The lines are perpendicular if their slopes are opposite reciprocals of each other. Or, if we multiply their slopes together, we get a product of [latex] - \,1 [/latex].

  17. Algebra 1

    The Students Will. Sketch the line given the equation. Sketch the line and find the slope and y-intercept given the equation. Sketch the line and write the equation for the line given the slope and the y-intercept.

  18. PDF Name LESSON 3.4 h Date rise For use with pages 171—179 Find the ope of

    Find the slope of each line. Are the lines Geometry Chapter 3 Practice Workbook 52 a . Name Practice LESSON For use with pages 171—179 Date CLQ Tell whether the lines through the given points are para e perpen ular, or neither. 10. Line 1: ... Geometry Chapter 3 Practice Workbook .

  19. Algebra 1 Worksheets

    Graphing Absolute Values Worksheets. These Linear Equations Worksheets will produce problems for practicing graphing absolute values. These Linear Equations Worksheets are a good resource for students in the 5th Grade through the 8th Grade. These Algebra 1 generator allows you to produce unlimited numbers of dynamically created linear equations ...

  20. Slope Assignment Find The Slope Of Each Line

    Slope Assignment Find The Slope Of Each Line - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Slope date period, Finding slope work, Find the slope level 1 s1, Assignment, Finding slope practice, Finding slope from a graph practice work, Slopeslope intercept form practice, Slope from two points.

  21. Slope Assignment Worksheets

    Slope Assignment - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Slope date period, Slope from two points, Types of slopes 1, Assignment, Find the slope level 1 s1, Infinite algebra 1, Lesson plan slope, Slope word problems.

  22. Assignment Find The Slope Of Each Line Worksheets

    Assignment Find The Slope Of Each Line - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Assignment, Slope date period, Finding slope practice, Find the slope level 1 s1, Slope from a, Assignment date period, Algebra 1, Math 1a calculus work.

  23. Algebra 1 Find The Slope Of Each Line Worksheets

    Algebra 1 Find The Slope Of Each Line - Displaying top 8 worksheets found for this concept. Some of the worksheets for this concept are Algebra 1 section work find the slope of the line, Slope, Slope from a, Infinite algebra 1, Keystone exams algebra i, Assignment, Algebra 1 name per work for 1 equation options, The slope of a line.