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EXAMPLE 1

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

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EXAMPLE 1

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

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

  3. MP3Players 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). EXAMPLE 3 Write an inverse variation model • Write a model that gives the number nof songs that will fit on the MP3 player as a function of the average song size s(in megabytes).

  4. • 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? EXAMPLE 3 Write an inverse variation model

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

  6. STEP 2 Make a table of values. ANSWER 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. EXAMPLE 3 Write an inverse variation model

  7. 0.75 y = x for Examples 1, 2 and 3 GUIDED PRACTICE Tell whether xand yshow direct variation, inverse variation, or neither. Type of Variation Given Equation Rewritten Equation Direct 1. 3x = y y = 3x 2.xy = 0.75 Inverse Neither 3.y = x –5

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

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

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

  11. 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. a n= s a 3000= 5 15,000 s ANSWER A model is n = for Examples 1, 2 and 3 GUIDED PRACTICE Write general equation for inverse variation. Substitute 3000 for n and 5 for s. 15,000 = a Solve for a.

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