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8.4 Slope

8.4 Slope. Objectives: To find the slope of a line given two points on the line To Find Slope Given an Equation of a Line To describe slope for horizontal and vertical lines. 10. 8. 6. 4. Slope =. 2. 10. 6. 8. -2. -4. 2. 4. -2. -4. -6. -8. -10. Slope. run. rise. 10. 8.

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8.4 Slope

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  1. 8.4 Slope Objectives: To find the slope of a line given two points on the line To Find Slope Given an Equation of a Line To describe slope for horizontal and vertical lines

  2. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope run rise

  3. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 1 Graph the line containing points (2,1) and (7,6) and find the slope. run rise

  4. Practice Graph the line containing these points and find their slopes. 1) (-2,3) (3,5) 2) (0,-3) (-3,2)

  5. Slope = Slope or

  6. Example 2 Find the slope of the line containing points (1,6) and (5,4).

  7. Practice Find the slope of the lines containing these points. 2) (-2,3) (2,1) 1) (2,2) (8,9) 3) (5,-11) (-9,4)

  8. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope of a Horizontal Line What about the slope of a horizontal line? What is the rise? 0 6 What is the run? The slope of ANY horizontal line is 0.

  9. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Slope of a Vertical Line What about the slope of a vertical line? What is the rise? 5 0 What is the run? The slope of ANY vertical line is undefined.

  10. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 1 Find the slope of the line y = -4.

  11. 10 8 6 4 Slope = 2 10 6 8 -2 -4 2 4 -2 -4 -6 -8 -10 Example 2 Find the slope of the line x = 7. The line has no slope.

  12. Practice Find the slopes, if they exist, of the lines containing these points. 1) (9,7) (3,7) 2) (4,-6) (4,0) 3) (2,4) (-1,5)

  13. Slope-Intercept Equation Find the slope of the line y = 2x - 4. 8 y = 2x - 4 6 4 2 0 -4 6 8 -2 1 -2 -8 -6 -4 2 4 -2 rise: -4 2 0 -4 run: -2 -6 -8 The y-intercept is -4.

  14. Slope-Intercept Equation y = mx + b y = 4x + 8 y = 2x - 3 slope y-intercept slope = 4 y-intercept = 8 slope = 2 y-intercept = -3

  15. Example 1 Find the slope and y-intercept of the line y = -4x + 4. The slope is -4. The y-intercept is 4.

  16. Example 2 Find the slope and y-intercept of the line y = 5x - 7. The slope is 5. The y-intercept is -7.

  17. Practice Find the slope and y-intercept of each line. • y = x + 3 • y = -4x – 7 • y = 3x - 9

  18. Example 3 Find the slope and y-intercept of the line 3x + 4y = 12. 3x + 4y = 12 solve for y -3x -3x 4y = 12 – 3x 4 4 slope y-intercept = 3

  19. Practice Find the slope and y-intercept of each line. • y = -x - 3 2) 8x + 2y = 10 3) 3y – 6x = 12

  20. Practice 2 Find the slope and y-intercept. • y = 3x + 4 2) y = -2x - 8 3) 2x + 7y = 9 4) 4x = 9y + 7

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