EXAMPLE 1 Classify direct and inverse variation Tell

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

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. a Write general equation for inverse variation. y= x a Substitute 7 for y and 4 for x. 7= 4 28 = a Solve for a. ANSWER 28 The inverse variation equation is y = x When x = – 2, y = 28 = – 14. – 2

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

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

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

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

GUIDED PRACTICE for Examples 1, 2 and 3 Tell whether x and y show direct variation, inverse variation, or neither. Given Equation Rewritten Equation Type of Variation 1. 3 x = y y = 3 x Direct 2. xy = 0. 75 y= x Inverse 3. y = x – 5 Neither

GUIDED PRACTICE for Examples 1, 2 and 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. 4. x = 4, y = 3 a y= x a 3= 4 12 = a Write general equation for inverse variation. Substitute 3 for y and 4 for x. Solve for a. ANSWER 12 The inverse variation equation is y = x 12 = 6. When x = 2, y = 2

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

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

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