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

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 = = = •

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.

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 =

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

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.

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.