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5.3 Direct Variation C

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5.3 Direct Variation C

  1. 1. Direct Variation Equations
  2. 2. Review What is the slope?
  3. 3. Slope = 1/2
  4. 4. Slope = -1
  5. 5. Slope = 5
  6. 6. Slope = Undefined
  7. 7. 65 mph 1. What was the greatest speed that Michael traveled?
  8. 8. Constant Speed 2. What does the horizontal segment of the graph represent? How long does Michael stay at this speed? 70 mins - 20 mins = 50 mins
  9. 9. Speed is decreasing 3. What does the segment with a negative slope tell you about Michael’s speed?
  10. 10. Speed is increasing 4. What does the segment with a positive slope tell you about Michael’s speed?
  11. 11. Vocabulary <ul><li>Direct Variation Equation – An equation of the form y = kx, where k does not equal zero </li></ul><ul><li>Constant of Variation – k in a direct variation equation </li></ul>
  12. 13. Example 2-1a Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer: The constant of variation is 2 . The slope is 2 . Slope formula Simplify.
  13. 14. Example 2-1b Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer: The constant of variation is –4 . The slope is –4 . Slope formula Simplify.
  14. 15. Example 2-1c Answer: constant of variation: 4 ; slope: 4 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a.
  15. 16. Example 2-1d Answer: constant of variation: –3 ; slope: –3 Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. b.
  16. 17. <ul><li>The constant of variation is the slope </li></ul>
  17. 20. Example 2-4a Find the value of k . 15 = k (5) Replace y with 15 and x with 5. 15 = k (5) 5 5 Divide each side by 5 3 = k Simplify Equation? y = 3x Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 5. Y = 15 when x = 5 Direct variation formula
  18. 21. Example 2-4a Find the value of k . 9 = k (3) Replace y with 15 and x with 5. 9 = k (3) 3 3 Divide each side by 5 3 = k Simplify Equation? y = 3x Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 7. Y = 9 when x = 3 Direct variation formula
  19. 22. Example 2-4a Find the value of k . 18 = k (11) Replace y with 15 and x with 5. 18 = k (11) 11 11 Divide each side by 5 18 = k Simplify 11 Equation? y = 18 x 11 Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 9. y = 18 when x = 11 Direct variation formula
  20. 23. Example 2-4a Find the value of k . 42 = k (7) Replace y with 15 and x with 5. 42 = k (7) 7 7 Divide each side by 5 6 = k Simplify Equation? y = 6x Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 11. y = 42 when x = 7 Direct variation formula
  21. 24. Example 2-4aExample 2-4cExample 2-5b Find the value of k . 12 = k (22) Replace y with 15 and x with 5. 12 = k (22) 22 22 Divide each side by 5 6 = k Simplify 11 Equation? y = 6 x 11 Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 13. y = 12 when x = 22 Direct variation formula
  22. 25. Example 2-5c Graph the equation. The graph of passes through the origin with a slope of 60 . Answer:

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