Log in Register

Login to your account

Username *
Password *
Remember Me

Create an account

Fields marked with an asterisk (*) are required.
Name *
Username *
Password *
Verify password *
Email *
Verify email *

Newsletter

Please select a list in the module configuration!No fields selected! Select at least "email"!

Changing an Equation into Slope-Intercept Form

Introduction

 

Before doing this lesson, you should have a grasp of the concept of slope as well as a good idea of how to use a table to draw lines on a coordinate plane.  See the menu of algebra links for lessons on these topics.


 

 

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.  However, not all equations are given in this form.

Change_into_SI_form_vis_0

Equations that are not in this form may be more difficult to graph.  Before looking at the lesson, consider the equation 8y = 24 – 4x.  Can you find any coordinates that work for this equation?  Can you determine the slope of this line or the x or y intercept?

 

Drawing the line of the equation 8y = 24 – 4x can be done, but this line can be graphed more easily if the equation is rewritten in slope-intercept form.  In this lesson, you will learn how to change equations into slope-intercept form to allow you to analyze them and draw their graph more easily.


Lesson

In the introduction, you were asked to take a closer look at the equation 8y = 24 – 4x.  Finding coordinates for this equation can be done by “plugging in” values of x.

Change_into_SI_form_vis_1 


If x = 0, then 8y = 24 and y = 3.  This is the coordinate (0, 3)

If x = 1, then 8y = 24 – (4)1, 8y = 20, and y = 2.5.  Coordinate (1, 2.5)

If x = 2, then 8y = 24 – (4)(2), 8y = 16 and y = 2.  Coordinate (2, 2)


 

Change_into_SI_form_vis_2 

 

 

The graph of the equation 8y = 24 – 4x is shown to the left.  The graph makes a straight line and this line appears to have a negative slope and a y-intercept of 3.  One can look at the graph and determine the slope and the y-intercept visually, but it is also possible to find these two characteristics of the line using algebra.

 

 

 

 

The slope-intercept form of an equation is y = mx + b, where m is the slope and b is the y-intercept.  To change our original equation into slope-intercept form, simply solve the equation for y.

Change_into_SI_form_vis_3

In the equation above, the y-term has been isolated on the left side of the equation and the right side has been rearranged into slope-intercept form (mx + b).  So the equation has been 8y = 24 – 4x can be changed into y = -½x + 3.  The slope is -½ and the y-intercept is 3.

 

Finding the slope and y-intercept of an equation can often be done without drawing a graph.  See if you can find the slope and y-intercept of the equation without drawing a graph.

 

Example 1: Find the slope and y-intercept of the line 5x + 5y = 10.

 

Change_into_SI_form_vis_4a1Solution:

Change_into_SI_form_vis_4


 

 

 

 

 

 

 

 

Example 2: Find the slope and y-intercept of the line 2y = 6(x + 3)

 

Change_into_SI_form_vis_5a1Solution:

Change_into_SI_form_vis_5

 

 

 

Examples 1 and 2 result in equations whose slopes and y-intercepts are integers.  When simplifying many equations, however, you will often run into fractions for the slope, y-intercept, or both.  Example 3 demonstrates fractional results for the slope and y-intercept.

 

Example 3: Find the slope and y-intercept of the line 5y = 24 + 8x

 

Solution:

Change_into_SI_form_vis_6

 

You can use the rules of algebra to change any 2-variable equation into slope-intercept form.  Remember that the simplified (slope-intercept) form can be useful to quickly identify the slope and y-intercept of the line.

 

 Even though graphing is not covered in this lesson, the purpose of changing an equation into slope-intercept form is often to draw the graph.  Drawing the graph of a line is easiest when the equation is in slope-intercept form. 

 

Try It

 

Find the slope and y-intercept for each equation: 

1)  3y = 3x + 9

2)  5(x + y) = 25

3)   2x = 4y + 8

4)  10x + 2y = 20

5)  4y = 13x - 20

 


Scroll down for answers…

 

 

 

 

 

 

 

Solutions:

1)  Solution:

Change_into_SI_form_vis_8

 

2)  Solution:

Change_into_SI_form_vis_9


3)  Solution:

Change_into_SI_form_vis_10


4)  Solution:

Change_into_SI_form_vis_11


5)  Solution:

Change_into_SI_form_vis_12

 

 

 

Related Links:

For more information on graphing lines and related topics, try one of the links below.

Resource Pages

 

Related Lessons

 

Looking for something else?  Try the buttons to the left or type your topic into the search feature at the top of this page.

Copyright © 2014. Free Math Resource.
All Rights Reserved.