Find the equation of variation for y = 30 when x = 5, where y varies inversely as x.

A. y = 6x

B. y = 150 x

C. y = x 150

D. y = 6 x

A.
Incorrect. The equation for inverse variation is y = k/x. Find the value of k by multiplying x and y.

B.
Correct! The value of k is 30 × 5 or 150.

C.
Incorrect. The equation for inverse variation is y = k/x.

D.
Incorrect. This is inverse variation. Find the value of k by multiplying x and y.

If y varies inversely as x and x = 18 when y = 6, find y when x = 8.

A. 13.5

B. 8 3

C. 24

D. 108

A.
Correct! The equation for inverse variation y = k/x was used, the value of k was found by multiplying 18 × 6 and the correct value of y is found when x = 8.

B.
Incorrect. The equation for inverse variation is y = k/x.

C.
Incorrect. The equation for inverse variation is y = k/x.

D.
Incorrect. This is the value of k. Now find the value of y when x = 8.

If y varies inversely as x, find y when x = -3 if the constant of variation is 1 6 .

A. - 1 2

B. - 2

C. - 1 18

D. - 18

A.
Incorrect. k = 1/6 and an equation for inverse variation is xy = k.

B.
Incorrect. k = 1/6 and an equation for inverse variation is xy = k.

C.
Correct! k = 1/6 and an equation for inverse variation is xy = k or -3x = 1/6 or y = -1/18.

D.
Incorrect. k = 1/6 and an equation for inverse variation is xy = k.

If y varies inversely as x and x = 3 when y = 20, find y when x = 15.

A. 0

B. 4

C. 60

D. 9 4

A.
Incorrect. The equation for inverse variation is y = k/x.

B.
Correct! The value of k is 60, therefore, y = 60/15 = 4.

C.
Incorrect. This is the value of k. Now find the value of y when x = 15.

D.
Incorrect. The equation for inverse variation is y = k/x.

The volume V of a gas varies inversely as the pressure p on it. If the volume is 300cm³ under a pressure of 48 kg cm² , find the volume under a pressure of 25 kg cm² .

A. 156.25 cm³

B. 14,400 cm³

C. 360,000 cm³

D. 576 cm³

A.
Incorrect. The value of k can be found by multiplying V and p. Use that value to find V.

B.
Incorrect. This is the correct k value. Use this value and p = 25 to find V.

C.
Incorrect. The value of k can be found by multiplying V and p. Use that value to find V.

D.
Correct! The correct value of k.