9.1 Inverse & Joint Variation9.1 Inverse & Joint Variation

Objectives/Assignment

Write and use inverse variation models

Write and us joint variation models

Assignment: 21-47 odd

Just a reminder from chapter 2Just a reminder from chapter 2

Direct VariationUse y=kx.

Means “y varies directlyvaries directly with x.”k is called the constant of variationconstant of variation.

Variationy

Notice k Directx

New stuff!

Inverse VariationInverse Variation

“y varies inverselyvaries inversely with x.”k is the constant of variationconstant of variation.

x

ky

xy = k Indirect VariationNotice

Ex: tell whether x & y show direct variation, inverse variation, or neither.

a. xy=4.8

b. y=x+4

c. 1.5

yx

Hint: Solve the equation for y and take notice of

the relationship.

xy

8.4

Inverse Variation

Neither

xy 5.1

Direct Variation

Ex: The variables x & y vary inversely, and y=8 when x=3.

• Write an equation that relates x & y.

k=24• Find y when x= -4.

y= -6

:k

use yx

3

8k

x

ky

24y

x

4

24

y

Joint Variation

• When a quantity varies directly as the product of 2 or more other quantities.

• For example: if z varies jointly with x & y, then z=kxy.

• Ex: if y varies inversely with the square of x, then y=k/x2.

• Ex: if z varies directly with y and inversely with x, then z=ky/x.

Examples: Write an equation.

• y varies directly with x and inversely with z2.• y varies inversely with x3.• y varies directly with x2 and inversely with z.• z varies jointly with x2 and y.• y varies inversely with x and z.

2

kxy

z

3

ky

x

2kxy

z

2z kx y

ky

xz