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.
- 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
.
- 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).
- Isolate they-variable, usually by adding a variable expression or a number to or subtract-
Once the equation is rewritten in slope-intercept form, it is easy to find the slope and
y-intercept by looking at the equation.
- 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