This document provides examples of calculating slope from points on a line. It defines slope as the rise over the run and gives the formula m = (y2 - y1) / (x2 - x1). Several examples show applying this formula to find the slope of a line given two points it passes through. One example calculates the average rate of change in temperature over time. Another finds the x-value that gives a line between two points a specific slope. The last example calculates the average yearly increase in radio stations from 1980 to 1994.

1. Module 4 Topic 2Slope of Linear Equations

2. Example 1Slope = mm = (y2 - y1) ÷ (x2 - x1) y2 = -3 y1 = 9 x2 = 7 x1 = 5 m = (-3 - 9) ÷ (7 - 5) m = -12 ÷ 2 m = -6

3. Example 2Similar Problem: Find the slope of the line that passes through the points (5, 9) and (7, -3).Slope = mm = (y2 - y1) ÷ (x2 - x1)y2 = -3y1 = 9x2 = 7x1 = 5m = (-3 - 9) ÷ (7 - 5)m = -12 ÷ 2m = -6

4. Example 3Similar Problem: Find the slope of the line that passes through the points (5, 9) and (7, -3).Slope = mm = (y2 - y1) ÷ (x2 - x1)y2 = -3y1 = 9x2 = 7x1 = 5m = (-3 - 9) ÷ (7 - 5)m = -12 ÷ 2m = -6

5. Example 4Similar Problem: You are camping at the Grand Canyon. When you pitch your tent at 4:00 P.M. the temperature is 93° F. When you go to bed at 10 P.M. the temperature is 63° F. What is the average rate of change in the temperature?Let's set up two ordered pairs (4, 93) and (10, 63).Use the ordered pairs to find the slope.(63 - 93) ÷ (10 - 4)-30 ÷ 6-5so the temperature has dropped 5° F every hour.

6. Example 5Similar Problem: Find the value of x so that the line passing through the points will have the given slope: (x, 8) and (6, 4) with a slope of -2/3.Slope = (y2 - y1) ÷ (x2 - x1)-2/3 = (4 - 8) ÷ (6 - x)-2/3 = -4 ÷ (6 - x)Cross multiply!!!!-2(6 - x) = 3(-4)-12 + 2x = -122x = 24x = 12

7. Example 6Similar Problem: What is the slope of the line that passes through the points (-3, 5) and (4, 5)?y2 = 5y1 = 5x2 = 4x1 = -3m = (5 - 5) ÷ (4 - (-3))m = 0 ÷ 7m = 0(Hint: Notice that the y's are the exact same value so the slope is going to be zero. If you were to graph these two points you would have a horizontal line which has a slope of zero).

8. Example 7Similar Problem: What is the slope of the line that passes through the points (4, 6) and (4, -3)?Slope = (-3 - 6) ÷ (4 - 4)Slope = -9 ÷ 0Slope = -9/0 which is undefined

9. Example 8Similar Problem: In 1980, there were 8.6 thousand radio stations on the air in the United States. In 1994, there were 11.2 thousand. What was the average rate of change per year in the number of radio stations in the United States from 1980 to 1994?Lets set up two ordered pairs (1980, 8.6) and (1994, 11.2)Use the two ordered pairs to find the slope.(11.2 - 8.6) ÷ (1994 - 1980)2.6 ÷ 140.1857 so 0.186 per year