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Variation

Variation. Chapter 9.1. Direct Variation. As x increases/decreases, y increases/decreases too. y = kx k is called the Constant of Variation k ≠ 0 “y varies direct with x” or “y varies directly as x”. Inverse Variation. x and y vary inversely if xy = k or

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Variation

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  1. Variation Chapter 9.1

  2. Direct Variation As x increases/decreases, y increases/decreases too. y = kx k is called the Constant of Variation k ≠ 0 “y varies direct with x” or “y varies directly as x”

  3. Inverse Variation x and y vary inversely if xy = k or k is still called the Constant of Variation and k ≠ 0 “y varies inversely with x” or “y varies inversely as x”

  4. Joint Variation Occurs when a quantity varies directly with two or more other quantities. z = kxy Again, k is the Constant of Variation and k ≠ 0 “z varies jointly with x and y”

  5. Summary Of Variation • Direct Variation y = kx • Inverse Variation • Joint Variation z = kxy • ***k is the Constant of Variation

  6. Determining Variation • Tell whether x and y show direct variation, inverse variation, or neither… • Solve for y • See if it matches one of the formulas: y = kx or • No match means “Neither”

  7. Determining Variation • Tell Whether the following is direct variation, inverse variation or neither

  8. Determining Variation • Tell Whether the following is direct variation, inverse variation or neither

  9. Determining Variation • Tell Whether the following is direct variation, inverse variation or neither

  10. Using Variation to Find Values • Given the Type of Variation and Values for x & y • Write the variation formula • Substitute the given values • Solve for k • Use the k you found to write a specific formula • Use this formula and given condition to solve for missing variable.

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