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Transcript
Lesson 12
Name: Writing a Linear Equation in Slope-Intercept Form
Study the example problem showing how to write an
equation in slope-intercept form. Then solve problems 1–6.
Example
y
Write an equation for the line shown in the
diagram.
8
7
6
Find the slope of the line.
y 2 y1 7 2 3 Use the slope formula.
 ​ 
 
5 ​ 
  
​
 
m 5 ​  2
x2 2 x1 ·····
2 2 0 Substitute 7 for y2, 3 for
······
y1, 2 for x2, and 0 for x1.
m 5 ​ 4 ​, or 2
2
··
Simplify. The slope is 2.
5
4
3
1
22 21 O
1
2
3
4
5
x
6
The line passes through (0, 3), so the
y-intercept is 3. Use the slope-intercept form
y 5 mx 1 b to write an equation.
y 5 mx 1 b
y 5 2x 1 3
Substitute 2 for m and 3 for b.
An equation for the line is y 5 2x 1 3.
1 How is the equation y 5 2x similar to the equation
y 5 2x 1 3 in the example problem? How is it different?
2 Graph y 5 2x in the diagram above. Compare the graphs.
Does either graph represent a proportional relationship?
Explain.
Vocabulary
slope  the ratio of the vertical
change (rise) to the horizontal
change (run) between any
two points on a line.
y-intercept  the y-coordinate
of the point where a graph
intersects the y-axis.
y
7
6
5
4
2
1
3 What value of b makes y 5 2x 1 b the same as y 5 2x?
What does that value mean?
©Curriculum Associates, LLC  Copying is not permitted.
(0, 3)
21 O
21
1
2
3
4
6
7
x
The y-intercept is 3.
Lesson 12  Understand the Slope-Intercept Equation for a Line
135