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

Teaching Notes 4.7: Identifying the Slope andY-Intercept

from an Equation

Two problems often arise when students are asked to identify the slope andy-intercept from an

equation. First, they may misinterpret the formula, and second, they may make an error rewriting

the equation.

1. Review the slope-intercept form of an equation,y=mx+b. Ask your students to iden-
   tify the slope andy-intercept using equations such asy= 3 x−1inwhichm=3,b=−1;
   y=− 2 xin whichm=−2,b=0; andy=

2

5

x−

1

3

in whichm=

2

5

,b=

− 1

3

.

2. Explain that sometimes students must rewrite an equation to express it in slope-intercept
   form. They should do the following:
   
   
   • Isolate they-variable, usually by adding a variable expression or a number to or subtract-
     ing a variable expression or a number from both sides.
   
   
   • Divide both sides of the equation by the coefficient ofy(unless the coefficient is 1).
   
   
   
   

Once the equation is rewritten in slope-intercept form, it is easy to find the slope and

y-intercept by looking at the equation.

3. Review the information and examples on the worksheet with your students. Explain that
   because the second example is not written in slope-intercept form, it must be rewritten.

EXTRA HELP:

If the slope is an improper fraction, do not change it to a mixed number.

ANSWER KEY:

(1)m=3;b=− 2 (2)m=3;b= 0 (3)m=

1

2

;b=− 6 (4)m=−1;b= 1

(5)m=

3

4

;b= 1 (6)m=2;b= 3 (7)m=

4

5

;b=− 2 (8)m=−

7

3

;b=

10

3

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(Challenge)They-intercept of each of the graphs is 0.

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150 THE ALGEBRA TEACHER’S GUIDE