4.5 The Slope of a Line
Goal
Find the slope of a line.
VOCABULARY
Slope
Example 1
The Slope Ratio
Find the slope of a ramp that has a vertical rise of 3 feet and a
horizontal run of 18 feet. Let m represent the slope.
Vertical Rise 3 feet
V
Horizontal Run 18 feet
Solution
m
Answer The slope of the ramp is
THE SLOPE OF A LINE
In the slope
formula, x1 is read
as “x sub one” and
y2 as “y sub two.”
The slope m of a line that passes
through the points ((x1, y1) and
( 2, y2) is
(x
change in
.
y
(xx2, y2)
y2 y1
(xx1, y1)
x2 x1
rise
m run
change in
x
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a division of Houghton Mifflin Company.
.
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Notetaking Guide
89
Example 2
Positive Slope
Find the slope of the line that passes through the points (1, 2)
and (2, 3).
( 2, y2) (2, 3).
Solution Let ((x1, y1) (1, 2) and (x
m
y
Formula for slope
(1, 2)
1
5
Substitute values.
3
1
1
1
3 x
(2,
2 3)
Simplify.
Slope is
Answer The slope of the line is
right. The slope is
Example 3
3
.
. The line
from left to
.
Zero Slope
Find the slope of the line passing through the points (2, 3)
and (4, 3).
( 2, y2) (4, 3).
Solution Let ((x1, y1) (2, 3) and (x
m
y
Formula for slope
1
3
Substitute values.
1
1
1
3
(
2, 3)
3
5 x
(4, 3)
3
5
Simplify.
Slope is
Answer The slope of the line is
Copyright © McDougal Littell,
a division of Houghton Mifflin Company.
3
.
. The line is
.
Chapter 4 • Algebra 1, Concepts and Skills
Notetaking Guide
90
Example 4
Undefined Slope
Find the slope of the line passing through the points (1, 4)
and (1, 2).
Solution
Let ((x1, y1) (1, 4) and ((x2, y2) (1, 2).
m
y
Formula for slope
3
1
3
(1,, 2)
2
1
1
3
x
Substitute values.
(1,, 4)
4
5
Division by
Answer Because division by
. The line is
is
is
.
.
, the slope is
Checkpoint Find the slope of the line passing through the
points. Then state whether the slope of the line is positive,
negative, zero, or undefined.
1. (5, 2), (7, 2)
2. (0, 0), (9, 0)
3. (7, 8), (7, 8)
4. (2, 4), (8, 6)
Copyright © McDougal Littell,
a division of Houghton Mifflin Company.
Chapter 4 • Algebra 1, Concepts and Skills
Notetaking Guide
91