2. Rate of Change and Slope

3. Quick Preview The diagram at the right shows the side view of a ski lift. 1.What is the vertical change from: a. A to B? b.B to C? c.C to D? 2.What is the horizontal change from: a.A to B? b.B to C? c.C to D

4. Rate of Change 5. What is the rate of change for the data to the left? 6. What does the rate of change mean in practical terms? How much the _____ (Y) increases per ____ (X)

5. The Magnum Cedar Point, OH Ghost Rider Knott’s Berry Farm Xcelerator Knott’s Berry Farm Superman 6 Flags Magic Mountain Son of Beast King’s Island, OH How steep is the steepest roller coaster? These are completely vertical!

6. Imagine a roller coaster moving from LEFT to RIGHT

7. There are four different kinds of slope the coaster could encounter...

10. And 2 Special Cases… The zero-fun totally lame snoopy coaster The impossibly scary totally awesome top thrill dragster coaster

11. Aw! That’s zero fun!

12. That’s a really scary coaster, so the slope is…

13. For the following slides, state whether the slope is positive, negative, zero, or undefined on your paper

14. 7. positive, negative, zero, or undefined?

15. 8. positive, negative, zero, or undefined?

16. 9. positive, negative, zero, or undefined?

18. How do you calculate the slope of a line? 1. Pick two points on the line 2. Calculate “rise over run” (be sure to put a negative if it’s going to the left)

19. Start with 2 points on gridline intersections

20. How do you calculate the slope of a line? Vertical change (∆Y) Horizontal change (∆X) OR... Rise Run m = M = Rise Run

21. 11. Find the slope of the following Graph: +

22. 12. Find the slope of the following Graph:

23. Slope Formula Example: Given (5, -3) and (-4, 2), find the slope of the line. x1x1 y1y1 x2x2 y2y2 12. Given (0, -2) and (4, -2), find the slope of the line.