11-1 Study Guide and Intervention (continued) Inverse Variation Inverse Variations Situations in which the values of decrease as the values of increase are examples of y x We say that varies inversely as or is inversely proportional to inverse variation. y x, y x. Inverse Variation Equation an equation of the form = where 0 xy k, k ≠ Example 1: Solve for Suppose you drive 200 miles without k. stopping. The time it takes to travel a distance varies = xy k Inverse variation equation inversely as the rate at which you travel. Let = speed x 12(3) = k x = 12 and y = 3 in miles per hour and = time in hours. Graph the y 36 = k Simplify. variation. Choose values for and which have a product of 36. x y, The equation = 200 can be used to represent the xy x y situation. Use various speeds to make a table. –6 x y 10 20 –12 20 10 30 6.7 –18 40 5 2 18 50 4 3 12 60 3.3 6 6 Example 2: Graph an inverse variation in which y varies inversely as and = 3 when = 12. x y x Exercises Graph each variation if varies inversely as y x. 1. = 9 when = 2. = 12 when = 4 3. = when = 5 y x y x y x –3 –25 4. = 4 when = 5 5. = when = 6. = 4.8 when = 5.4 y x y x y x –18 –9
11-1 Study Guide and Intervention (continued) Inverse Variation Inverse Variations Situations in which the values of y decrease as the values of x increase are examples of inverse variation. We say that y varies inversely as x, or y is inversely proportional to x. Inverse Variation Equation an equation of the form xy = k, where k ≠ 0 Example 1: Suppose you drive 200 miles without stopping. The time it takes to travel a distance varies inversely as the rate at which you travel. Let x = speed in miles per hour and y = time in hours. Graph the variation. The equation xy = 200 can be used to represent the situation. Use various speeds to make a table. x y 10 20 20 10 30 6.7 40 5 50 4 60 3.3 Example 2: Graph an inverse variation in which y varies inversely as x and y = 3 when x = 12. Solve for k. xy = k Inverse variation equation 12(3) = k x = 12 and y = 3 36 = k Simplify. Choose values for x and y, which have a product of 36. x y –6 –12 –18 2 18 3 12 6 6 Exercises Graph each variation if y varies inversely as x. 1. y = 9 when x = –3 2. y = 12 when x = 4 3. y = –25 when x = 5 4. y = 4 when x = 5 5. y = –18 when x = –9 6. y = 4.8 when x = 5.4
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