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Variation

Variation. Objective: Apply algebraic techniques to rate problems. Vocabulary. Direct Variation. Constant of Variation. #1 Find an equation of variation where y varies directly as x. #2 Find an equation of variation where y varies directly as x. k = 5/8. y = 5/8x. Vocabulary.

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Variation

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  1. Variation Objective: Apply algebraic techniques to rate problems.

  2. Vocabulary • Direct Variation Constant of Variation

  3. #1 Find an equation of variation where y varies directly as x.

  4. #2 Find an equation of variation where y varies directly as x. k = 5/8 y = 5/8x

  5. Vocabulary • Inverse Variation

  6. #3 Find an equation of variation where y varies inversely as x.

  7. #4 Find an equation of variation where y varies inversely as x.

  8. #5 Solve the problem using direct variation. • The Weight (V) of an object on Venus varies directly as its weight (E) on Earth. A person weighing 120 lb on Earth would weigh 106 lb on Venus. How much would a person weighing 150 lb on Earth weigh on Venus?

  9. #5 Solve the problem using direct variation.

  10. #6 Solve the problem using inverse variation. • The time (t) required to drive a fixed distance varies inversely as the speed (r). It takes 5 hours at 60 km/h to drive a fixed distance. How long would it take to drive the same distance at 40 km/h?

  11. #6 Solve the problem using direct variation.

  12. Vocabulary • Joint Variation

  13. #7 Find an equation of variation where w varies jointly as x, y, and z.

  14. #8 Find an equation of variation where Q varies jointly as R and S.

  15. Vocabulary • Combined Variation

  16. #9 Find an equation of combined variation where P varies directly as q and inversely as r.

  17. #10 Solve the problem using combined variation. • Find an equation of combined variation where A varies directly as b and inversely as c. One set of values is A = 4, b = 12, and c= 9. Find A when b = 7 and c = 3.

  18. #10 Solve the problem using combined variation.

  19. #11 Solve the problem using variation. • The interest earned at Whole World Savings & Loan varies jointly as the amount deposited in the bank and the time elapsed since the deposit. If a $500 deposit earns $120 interest after 3 years, how much does an $800 deposit earn after 5 years?

  20. #11 Solve the problem using variation.

  21. You TRY #1-7

  22. Solutions: • 1. k = 48, y = -8 • 2. k = 24, x = -12 • 3. k = 75, y = 25/3 • 4. k = 2, r = 4 • 5. k = 3, y = -36 • 6. k = 4, x = 6 • 7. k = ∏, r = 3

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