What You Will Learn

• Recognize and solve direct and joint variation problems

• Recognize and solve inverse variation problems

1) Direct Variation

2) Joint Variation

3) Inverse Variation

Direct Variation• Can be expressed in the form y=kx

• K in this equation is called constant of variation

• Slope of a direct variation = constant of variation.

• As x increases, y increases or decreases at a constant rate (y varies directly as x)

• If you know [y varies directly as x] and one set of values, you can use a proportion to find the other set of corresponding values.

kx

y

kxy

1

1

11

2

2

1

1

x

y

x

y

kx

y

kxy

2

2

22

2

2

1

1

x

y

x

y

163

12 2y

)(3)12(16 2y

264 y23192 y

Joint Variation• When 1 quantity varies directly as

the product of two or more other quantities.

• Y varies jointly as x and z if there is some number k such that y=kxz

• If you know y varies jointly as x and z and one set of values, you can use a proportion to find the other set of corresponding values.

22

2

11

1

zx

y

zx

y

Suppose y varies jointly as x and z. Find y when x=8 and z=3, if y=16 when z=2 and x =5.

22

2

11

1

zx

y

zx

y

)3(8)2(5

16 2y

))(2(5)16)(3(8 2y

210384 y

24.38 y

Joint Variation

Cross Multiply

Divide by 10

Substitute numbers into the Joint Variation

Inverse Variation• As one quantity increases, the other

quantity decreases.

• If there is a nonzero constant k, xy=k or y=

x

k

Speed and time vary inversely with each other because when you travel somewhere, as your speed increases, the time it takes you to get there decreases.

1

2

2

1

y

x

y

x

311

18 2

r

)(11)3(18 2r

21154 r

211

104 r

1

2

2

1

t

r

t

r

Homework! =)

• Page 496 # 14-40 odd

• What is special about the # 496?