1. Simplify. Exercise 4 − 2 5 − 2 2323 2323

2. Simplify. 5 − 2 4 − 2 3232 3232 Exercise

3. Simplify. 2 − 4 5 − 2 Exercise 2323 2323 – –

4. Simplify. 2 − 4 2 − 5 2323 2323 Exercise

5. Simplify. 2 − 2 5 − 2 0 0 Exercise

6. Simplify. 4 − 2 2 − 2 undefined Exercise

7. The rise is the vertical change from point P 1 to point P 2 on a line. Rise

8. The run is the horizontal change from point P 1 to point P 2 on a line. Run

9. The slope of a line is the ratio of the rise to the run. The variable m is often used for slope. Slope

10. y y x x

11. y y x x

12. up to rightpositive down to rightnegative horizontalzero verticalundefined Slope

13. Slope = m = rise run

14. y y x x −3 1 1 Find the slope of the given line. m = = −3 −3 1 Example 1

15. If a line contains the points P 2 (x 2, y 2 ) and P 1 (x 1, y 1 ), then m = vertical change y 2 − y 1 horizontal change x 2 − x 1 = = Slope Formula

16. Find the slope of the line that contains the points (1, 2) and (7, 5). m = = y 2 − y 1 x 2 − x 1 5 − 2 7 − 1 = = 3636 3636 = = 1212 1212 Example 2

17. Find the slope of CD passing through (5, 3) and (2, 5). m = = y 2 − y 1 x 2 − x 1 5 − 3 2 − 5 = = 2 −3 = − 2323 2323 Example 3

18. Find the slope of EF passing through (3, 2) and (−1, 2). m = = y 2 − y 1 x 2 − x 1 2 − 2 −1 − 3 = = 0 −4 = 0 Example 4

19. y y x x (−1, 2) (3, 2)

20. = = 4040 4040 Find the slope of the line passing through the points (2, 1) and (2, 5). m = = y 2 − y 1 x 2 − x 1 5 − 1 2 − 2 Example 5

21. y y x x (2, 5) (2, 1)

22. m = 3 Graph and determine the slope of the following lines. y = 3x + 5 Example

23. 1212 1212 y = − x + 2 Graph and determine the slope of the following lines. m = − 1212 1212 Example

24. 2323 2323 y = x − 1 Graph and determine the slope of the following lines. m = 2323 2323 Example

25. m = 0 Graph and determine the slope of the following lines. y = 4 Example

26. m = −3 Graph and determine the slope of the following lines. y = −3x + 6 Example

27. undefined Graph and determine the slope of the following lines. x = 4 Example

28. They are the same. Compare the slopes of the lines in the previous questions to the coefficients of x. Example

29. m = 5252 5252 Find the slope of the line through (3, 7) and (5, 12). Example

30. m = −6 Find the slope of the line through (2, 3) and (4, −9). Example

31. m = 0 Find the slope of the line through (2, 5) and (3, 5). Example

32. m = undefined Find the slope of the line through (1, 1) and (1, 2). Example

33. Their slopes are the same and the lines are parallel. Graph the following lines and describe their graphs: y = 3x − 4, y = 3x, and y = 3x + 2. Example