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Published byCharity Kimbel Modified about 1 year ago

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EXAMPLE 1 Classify direct and inverse variation Tell whether x and y show direct variation, inverse variation, or neither. Given EquationRewritten Equation Type of Variation a. xy = 7 y = 7 x Inverse b. y = x + 3 Neither y 4 c. = x y = 4x Direct

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EXAMPLE 2 Write an inverse variation equation The variables x and y vary inversely, and y = 7 when x = 4. Write an equation that relates x and y. Then find y when x = –2. y = y = a x Write general equation for inverse variation. Substitute 7 for y and 4 for x. 7 = 7 = a 4 28 = a Solve for a. The inverse variation equation is y = 28 x When x = –2, y = 28 –2 = –14. ANSWER

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EXAMPLE 3 Write an inverse variation model The number of songs that can be stored on an MP3 player varies inversely with the average size of a song. A certain MP3 player can store 2500 songs when the average size of a song is 4 megabytes (MB). MP3 Players Write a model that gives the number n of songs that will fit on the MP3 player as a function of the average song size s ( in megabytes ).

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EXAMPLE 3 Write an inverse variation model Make a table showing the number of songs that will fit on the MP3 player if the average size of a song is 2MB, 2.5MB, 3MB, and 5MB as shown below. What happens to the number of songs as the average song size increases?

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EXAMPLE 3 Write an inverse variation model STEP 1 Write an inverse variation model. a n =n = s Write general equation for inverse variation. a 2500 = 4 Substitute 2500 for n and 4 for s. 10,000 = a Solve for a. A model is n = s 10,000 ANSWER

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EXAMPLE 3 Write an inverse variation model STEP 2 Make a table of values. From the table, you can see that the number of songs that will fit on the MP3 player decreases as the average song size increases. ANSWER

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GUIDED PRACTICE for Examples 1, 2 and 3 Tell whether x and y show direct variation, inverse variation, or neither. 1. 3x = y 2. xy = y = x –5 Given EquationRewritten Equation Type of Variation y = 3x Direct y = x 0.75 Inverse Neither

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GUIDED PRACTICE for Examples 1, 2 and 3 4. x = 4, y = 3 The variables x and y vary inversely. Use the given values to write an equation relating x and y. Then find y when x = 2. y = y = a x Write general equation for inverse variation. Substitute 3 for y and 4 for x. 4 3 = 3 = a 12 = a Solve for a. 12 x The inverse variation equation is y = When x = 2, y = 12 2 = 6. ANSWER

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GUIDED PRACTICE for Examples 1, 2 and 3 5. x = 8, y = –1 a y = x Write general equation for inverse variation. Substitute – 1 for y and 4 for x. –1 = a 8 – 8 = a Solve for a. – 8 ANSWER The inverse variation equation is y = – 8 x When x = 2, y = = – 4. 2

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GUIDED PRACTICE for Examples 1, 2 and 3, 6. x = 1 2 y = 12 Write general equation for inverse variation. 6 = a Solve for a. The inverse variation equation is y = 6 x When x = 2, y = 6 = 3. ANSWER 2 y = x a a 12 = 1 2 Substitute 12 for y and for x. 1 2

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GUIDED PRACTICE for Examples 1, 2 and 3 7. What If? In Example 3, what is a model for the MP3 player if it stores 3000 songs when the average song size is 5MB ? Write an inverse variation model. n =n = a s Write general equation for inverse variation. a 3000 = 5 Substitute 3000 for n and 5 for s. 15,000 = a Solve for a. A model is n = s 15,000 ANSWER

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