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Direct Variation Equations

Direct Variation Equations. Review What is the slope?. Slope = 1/2. Slope = -1. Slope = 5. Slope = Undefined. 65 mph. 1. What was the greatest speed that Michael traveled?. Constant Speed.

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Direct Variation Equations

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  1. Direct Variation Equations

  2. ReviewWhat is the slope?

  3. Slope = 1/2

  4. Slope = -1

  5. Slope = 5

  6. Slope = Undefined

  7. 65 mph 1. What was the greatest speed that Michael traveled?

  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. Speed is decreasing 3. What does the segment with a negative slope tell you about Michael’s speed?

  10. Speed is increasing 4. What does the segment with a positive slope tell you about Michael’s speed?

  11. Vocabulary • Direct Variation Equation – An equation of the form y = kx, where k does not equal zero • Constant of Variation – k in a direct variation equation

  12. Slope formula Simplify. Example 2-1a Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points. Answer: The constant of variation is 2.The slope is 2.

  13. Slope formula Simplify. Example 2-1b Name the constant ofvariation for the equation.Then find the slope of theline that passes through thepair of points. Answer: The constant of variation is –4.The slope is –4.

  14. Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. a. Example 2-1c Answer: constant of variation: 4; slope: 4

  15. b. Example 2-1d Name the constant of variation for the equation. Then find the slope of the line that passes through the pair of points. Answer: constant of variation: –3; slope: –3

  16. The constant of variation is the slope

  17. Example 2-4a Direct variation formula Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 5. Y = 15 when x = 5 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

  18. Example 2-4a Direct variation formula Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 7. Y = 9 when x = 3 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

  19. Example 2-4a Direct variation formula Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 9. y = 18 when x = 11 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 = 18x 11

  20. Example 2-4a Direct variation formula Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 11. y = 42 when x = 7 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

  21. Example 2-4aExample 2-4cExample 2-5b Direct variation formula Y varies directly as x. Find the constant of variation and write an equation for the direct variation. 13. y = 12 when x = 22 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

  22. The graph of passes through the origin with a slope of 60. Answer: Example 2-5c Graph the equation.

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