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Simplify.

2 3. Exercise. Simplify. 4 − 2 5 − 2. 3 2. Exercise. Simplify. 5 − 2 4 − 2. Exercise. Simplify. 2 3. 2 − 4 5 − 2. –. 2 3. Exercise. Simplify. 2 − 4 2 − 5. Exercise. Simplify. 2 − 2 5 − 2. 0. Exercise. Simplify. 4 − 2 2 − 2. undefined. Rise.

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Simplify.

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  1. 23 Exercise Simplify. 4 − 25 − 2

  2. 32 Exercise Simplify. 5 − 24 − 2

  3. Exercise Simplify. 23 2 − 45 − 2 –

  4. 23 Exercise Simplify. 2 − 42 − 5

  5. Exercise Simplify. 2 − 25 − 2 0

  6. Exercise Simplify. 4 − 22 − 2 undefined

  7. Rise The rise is the vertical change from point P1 to point P2 on a line.

  8. Run The run is the horizontal change from point P1 to point P2 on a line.

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

  10. y x

  11. y x

  12. Slope up to right positive down to right negative horizontal zero vertical undefined

  13. riserun Slope = m =

  14. m = = −3 −3 −31 1 Example 1 Find the slope of the given line. y x

  15. vertical change y2 − y1horizontal change x2 − x1 = Slope Formula If a line contains the points P2 (x2, y2) and P1 (x1, y1), thenm =

  16. y2 − y1x2 − x1 5 − 2 7 − 1 m = = 36 12 = = Example 2 Find the slope of the line that contains the points (1, 2) and (7, 5).

  17. y2 − y1x2 − x1 5 − 3 2 − 5 m = = 2−3 23 = = − Example 3 Find the slope of CD passing through (5, 3) and (2, 5).

  18. 2 − 2 −1 − 3 y2 − y1x2 − x1 m = = 0−4 = Example 4 Find the slope of EF passing through (3, 2) and (−1, 2). = 0

  19. y (−1, 2) (3, 2) x

  20. y2 − y1x2 − x1 5 − 1 2 − 2 m = = 40 = Example 5 Find the slope of the line passing through the points (2, 1) and (2, 5).

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

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

  23. y = − x + 2 12 12 m = − Example Graph and determine the slope of the following lines.

  24. y = x − 1 23 23 m = Example Graph and determine the slope of the following lines.

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

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

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

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

  29. 52 m = Example Find the slope of the line through (3, 7) and (5, 12).

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

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

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

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

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