1. 8 3 . Slope You can use ratios to describe the slope of a line.
L E S S O N
8 3 .
Slope
You can use ratios to describe the slope of a line.
Activity 1
Draw an x-axis and a y-axis on graph paper. y 2 1 2 3 4 5 6 7 8 9 10
Start at the origin. Move 2 units to the right and 3 units up. Plot this point and label it A. B 3
Rise = 6
Start at A. Move 4 units to the right and 6 units up. Plot this point and label it B.
Run = 4 A 4
Draw a line through A, B, and the origin.
Rise = 3 5
Find the ratio of rise to run for each of the movements described in Steps 2 and 3. O x 1 2 3 4 5 6 7
Run = 2

2. Slope
L E S S O N
8 3 .
The slope of a nonvertical line is the ratio of the rise (vertical change) to the run (horizontal change) between any two points on the line, as shown below. A line has a constant slope. x y O 1 2 3 4 5 6 7 8 •
run = 5
rise
run –2 5 2 5 –
rise = –2
slope = = = •

3. Slope
L E S S O N
8 3 .
The slope of a nonvertical line is the ratio of the rise (vertical change) to the run (horizontal change) between any two points on the line, as shown below. A line has a constant slope. y 4 •
run = 5 3
rise
run –2 5 2 5 2
rise = –2
slope = = = – • 1 x O 1 2 3 4 5 6 7 8
A line that rises from left to right has a positive slope.
A line that falls from left to right has a negative slope.
A horizontal line has a slope of 0.

4. 8 3 • • . 1 Slope Finding the Slope of a Line
L E S S O N
8 3 .
EXAMPLE 1
Finding the Slope of a Line
To find the slope of a line, find the ratio of the rise to the run between two points on the line. O x y 1 2 3 4 5 6 7 • 2 • 4
rise
run 2 4
slope = = 1 2 =

5. 8 3 • • • • . 1 Slope Finding the Slope of a Line
L E S S O N
8 3 .
EXAMPLE 1
Finding the Slope of a Line
To find the slope of a line, find the ratio of the rise to the run between two points on the line. y O x y 3 4 5 –3 –2 6 5 • • 3 4 3 2 • –3 2 4 • O 1 2 3 4 5 6 7 x
rise
run 2 4
rise
run –3 3
slope = =
slope = = 1 2 =
= –1

6. 8 3 . 2 Slope Interpreting Slope as a Rate
L E S S O N
8 3 .
EXAMPLE 2
Interpreting Slope as a Rate
Volcanoes The graph represents the distance traveled by a lava flow over time. To find the speed of the lava flow, find the slope of the line.
rise
run
6 mi
4 h
slope = =
Write rise over run.
1.5 mi
1 h =
Find unit rate.
ANSWER
The speed of the lava flow is 1.5 miles per hour.

7. 8 3 . 3 Slope Using Slope to Draw a Line
L E S S O N
8 3 .
EXAMPLE 3
Using Slope to Draw a Line
Draw the line that has a slope of –3 and passes through (2, 5). 1
Plot (2, 5). y 4 5 6 O 3 2 1 2
Write the slope as a fraction. 1 =
rise
run –3 1 =
slope –3 3
Move 1 unit to the right and 3 units down to plot the second point. x 1 2 3 4 5 6 4
Draw a line through the two points.