• direct variation

• constant of variation

• joint variation

• inverse variation

• combined variation

Direct Variation

If y varies directly as x and y = –15 when x = 5, find y when x = 3.

Use a proportion that relates the values.

Cross multiply.

y1 = –15, x1 = 5, and x2 = 3

Direct Variation

Direct Variation

–45 = 5y2 Simplify.

–9 = y2 Divide each side by 5.

Answer: When x = 3, the value of y is –9.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

If y varies directly as x and y = 12 when x = –3, find y when x = 7.

A. –28

B.

C.

D.

Joint Variation

Suppose y varies jointly as x and z. Find y when x = 10 and z = 5, if y = 12 when x = 3 and z = 8.

Use a proportion that relates the values.

Joint variation

y1 = 12, x1 = 3, z1 = 8,x2 = 10, and z2 = 5

Cross multiply.

Joint Variation

600 = 24y2 Simplify.

Answer: When x = 10 and z = 5, y = 25.

25 = y2 Divide each side by 24.

A. A

B. B

C. C

D. D A B C D

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Suppose y varies jointly as x and z. Find y when x = 3 and z = 2, if y = 11 when x = 5 and z = 22.

A.

B.

C.

D.

Inverse Variation

If r varies inversely as t and r = –6 when t = 2, find r when t = –7.

Inverse Variation

r1 = –6, t1 = 2, and t2 = –7

Cross multiply.

Inverse Variation

Simplify.

Divide each side by –7.

Answer: When t = –7, r is .

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

If a varies inversely as b and a = 3 when b = 8, find a when b = 6.

A.

B. 4

C. 16

D. 144

Combined Variation

Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –5, if g = 18 when h = 3 and f = 5.

First, set up a correct proportion for the information given.

g varies directly as f, so ggoes in the numerator. hvaries inversely as f, so hgoes in the denominator.

Solve for k.

Combined Variation

f1 = 5, h1 = 3, g1 = 18, f2 = 6, and h2 = –5

Set the two proportions equal to each other.

Cross multiply.

Simplify.

Divide each side by 15.

Answer: When f = 6 and h = –5, the value of g is –36.

A. A

B. B

C. C

D. D A B C D

0% 0%0%0%

A. –30

B. 30

C. 36

D. 40

Suppose f varies directly as g, and f varies inversely as h. Find g when f = 6 and h = –16, if g = 10 when h = 4 and f = –6.