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Understanding Direct, Inverse, Joint, and Combined Variation in Algebra

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This guide covers the principles of variation in algebra, focusing on direct, inverse, joint, and combined variations. Learn to identify and formulate equations of variation based on specific relationships. Practical examples illustrate how to apply algebraic techniques to real-world problems, such as calculating weights on different planets and understanding speed-time relationships. Additionally, explore joint and combined variation to solve complex equations related to interest and deposits in financial contexts. Enhance your algebraic skills and problem-solving abilities with this comprehensive overview.

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Understanding Direct, Inverse, Joint, and Combined Variation in Algebra

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  1. 12.5 – 12.7 Variation CA Standard 15.0 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.

  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.

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