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Notes 25

Notes 25. Inverse Variation. Vocabulary. Inverse variation- a relationship between two variables that can be written in the form y = k / x or xy = k , where k is a nonzero constant and x  0.

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Notes 25

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  1. Notes 25 Inverse Variation

  2. Vocabulary Inverse variation- a relationship between two variables that can be written in the form y =k/x or xy = k, where k is a nonzero constant and x 0.

  3. Inverse variation is a relationship between two variables that can be written in the form y =k/x or xy = k, where k is a nonzero constant and x 0. In an inverse variation, the product of x and y is constant.

  4. Additional Example 1A: Identifying an Inverse Variation Tell whether each relationship is an inverse variation, a direct variation or neither. Explain. Find y/x for each pair. The data represents a direct variation where k = 3.

  5. Additional Example 1B: Identifying an Inverse Variation Tell whether each relationship is an inverse variation, a direct variation or neither. Explain. Find the product xy. 3(40) = 120 4(30) = 120 5(24) = 120 The data represents a inverse variation where k = 120.

  6. Check It Out: Example 1A Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

  7. Check It Out: Example 1B Tell whether each relationship is an inverse variation, a direct variation, or neither. Explain.

  8. Additional Example 2: Application Eliza is building a rectangular patio. She has cement to cover 72 square feet. Write an inverse variation equation to find the width of the patio for lengths 4, 6, and 8 feet. xy = k xy = k xy = k Use xy = k. 4y = 72 6y = 72 8y = 72 Substitute for x and k. y = 18 y = 12 y = 9 An inverse variation equation is xy = 72. Eliza can build a 4 ft by 18 ft, 6 ft by 12 ft, or 8 ft by 9 ft patio.

  9. Check It Out: Example 2 A pizzeria makes rectangular pizzas. One ball of dough can cover 36 square inches. Write an inverse variation equation to represent the length of the pans for widths 3, 4, and 6 inches.

  10. Additional Example 3: Identifying a Graph of an Inverse Variation Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain. Identify points on the graph. Use the equation xy = k. (1)2= 2, (2)3 = 6 The values of k are not constant. The graph does not represent an inverse variation.

  11. Additional Example 3 Continued Tell whether each graph represents an inverse variation, a direct variation, or neither. Explain. Identify points on the graph. Use the equation y/x = k. 1/1 = 1, 2/1 = 2 The values of k are not constant. The graph does not represent an direct variation. The graph is neither.

  12. Check It Out: Example 3 Tell whether the graph represents an inverse variation, a direct variation, or neither. Explain. Field Trip 10 9 8 7 Number of Chaperones 6 5 4 3 2 1 0 15 5 10 20 25 Number of Students

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