1. Find Slope and Rate of Change Chapter 2.2

2. How Fast is He Walking?

5. Rate of Change In this second animation, the man’s speed is itself changing after every second passes The first animation is an example of a constant rate of change The second animation is an example of a variable rate of change (which means that the rate itself changes) The graph of two related quantities (like distance and time when something is moving) will be a line if the rate of change is constant This rate of change is commonly called the slope

6. Rate of Change

7. Slope of a Line

10. Example

11. Guided Practice

13. Classifying Lines by Slope You should be able to tell by looking at a line whether its slope is positive, negative, zero, or undefined Vertical lines have undefined slopes because, using the slope formula, the denominator yields zero and division by zero is not defined Horizontal lines have zero slopes because, using the slope formula, the numerator yields zero and every non-zero number divided by zero is zero For the last two cases, imagine that you are walking on a line from left to right in the coordinate plane

14. Negative Slope

16. Positive Slope

18. Classification of Line by Slope A vertical line has an undefined slope A horizontal line has a slope of zero A line that falls from left to right has a negative slope A line that rises from left to right has a positive slope

19. Example

20. Guided Practice

22. Parallel & Perpendicular Lines Recall from geometry that Two lines are parallel if they never intersect Two lines are perpendicular if they intersect at right angles (90˚) It is possible to show how the slopes of lines that are parallel or lines that are perpendicular are related, but this is lengthy so we will just remember the relationship

23. Parallel & Perpendicular Lines

24. Example

27. Guided Practice

30. Rate of Change At the beginning of this presentation, we considered slope as the ratio of the change in the distance a man walked compared to the time that passed The slope of a line is always the ratio of the change in one quantity compared to the change in another That is, slope is an average rate of change

31. Example

32. Guided Practice A Giant Sequoia tree has a diameter of 248 inches in 1965 and a diameter of 251 inches in 2005. Find the average rate of change in the diameter. Include units in your answer.

33. Guided Practice

34. Exercise 2.2 Page 86, #3-39 odds