1. Find Slope and Rate of Change Find Slope and Rate of Change Objective: Students will be able to find the slope of a line and interpret slope as a rate of change

2. Motivation Have you ever been skiing or seen it on television? What is the difference between the beginner’s trail, often called the bunny slope, and the expert’s trail, often called the black diamond slope? The black diamond slope will be much steeper than the bunny slope.

3. Definitions Slope- a ratio of the change in the y- coordinates to the change in the x- coordinates. Shows how steep a line is. Rate of Change- a ratio that describes how much one quantity changes with respect to a change in another quantity

4. Slope Symbol “m” m= Rise = Change in y Run Change in x Form: m = y 2 - y 1 x 2 – x 1 (x 1,y 1 ), (x 2,y 2 )

5. Find the Slope of the Line

6. Positive Slope m › 0 line rises from left to right y x

7. Find the Slope of the Line

8. Negative Slope m < 0 line falls from left to right y x

9. Find the Slope of the line that passes through the points (-3,-1) and (2,-1)

10. Slope of Zero m = 0 Horizontal Line y x

11. Find the slope of the line that passes through the points (-2,4) and (-2,-3)

12. Undefined Slope m = undefined Vertical Line y x

13. List the 4 Ways we can classify the slope of a Line Positive Negative Zero Slope Undefined

14. Rate of Change Rate of change = Change in y Change in x

15. Rate of Change Use the table to find the rate of change. Then explain its meaning. Number of computer games Total Cost(s) x y 278 4156 6234

16. The table shows the cost of using a computer at an internet café for a given amount of time. Find the rate of change in cost with respect to time. Time (hours)246 Cost (dollars)71421 Find the Rate of Change

17. (5, 4) (1, 2) Then count horizontally to the second point to find the run. Find the slope of the line. Begin at one point and count vertically to find the rise. slope = = 2424 1212 The slope of the line is 1212 Slope of a Line

18. (3, 2) (–1, –2) Then count horizontally to the second point to find the run. Find the slope of the line. Begin at one point and count vertically to find the rise. slope = = 1 4444 The slope of the line is 1. Slope of a Line

19. Your Turn to Have Fun!