The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 4.11: Using Slope-Intercept Form to

Graph the Equation of a Line

A linear equation written in slope-intercept form,y=mx+b, can easily be used to create a

graph. The slope of the line ismand they-intercept isb. Students may confuse these two

variables or inaccurately use the slope to graph the equation of the line.

1. Explain that slope-intercept form,y=mx+b, is one way to write an equation of a line.
   mrepresents the slope of the line andbrepresents they-intercept.


2. Present the equationy= 3 x+2. Have your students identify the slope andy-intercept. (The
   slope is 3 and they-intercept is 2.)


3. Show your students how to graph this equation. Begin by plotting point (0, 2), which is the
   y-intercept. Then use the slope to plot the next point. Because the slope is 3, which can be
   expressed as

3

1

, students would move up three units and one unit to the right. Also, because

3 may be expressed as

− 3

− 1

, students could move down three units and one unit to the left.

These movements are commonly referred to ashorizontal movementvertical movement orriserun.

4. Review the information on the worksheet with your students.

EXTRA HELP:

Always express the slope as a fraction. It is easier to apply rise over run.

ANSWER KEY:

(1)A, slope=3,y-intercept= 4 (2)F, slope=−1,y-intercept=− 1

(3)D, slope=2,y-intercept= 1 (4)B, slope=1.5,y-intercept= 3

(5)C, slope=2,y-intercept=− 1 (6)E, slope=−3,y-intercept= 4

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(Challenge)Both equations represent the same slope andy-intercept. Joe’s equation is written in

slope-intercept form, and Brian’s is written in standard form. However, each equation represents

thesameline.

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158 THE ALGEBRA TEACHER’S GUIDE