Inverse VariationInverse Variation

Do you remember?Do you remember?

Direct VariationUse y = kx.

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

In a situation like this, when one quantity goes up, the other goes up. When one quantity goes

down, the other goes down also.

Example of direct variation

• Tom makes $10 an hour. His wages vary directly to his hours

• Rope is sold by the foot. The cost of buying rope varies directly to the amount you buy.

Inverse VariationInverse Variation

when one quantity goes up, the other goes down proportionately.

When one quantity goes down, the other goes up by the some proportion.

Inverse VariationInverse Variation

This relationship is described as“y varies inverselyvaries inversely with x.”

And can be represtented by

k is the constant of variationconstant of variation.

x

ky

Example of inverse variation

• The time an ice block takes to melt varies inversely with the room temperature.

• In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board.

Ex 1. Y varies inversely as x, and y = 4 when x = 7.

Find x when y = 14

1. Write an equation that relates x & y.

k=282. Find y when x= -4.

y= -7

47

k

x

ky

28y

x

28

4y

Solve the problem in two parts.

1. Use the inverse variation equation to find k when they give you both x and y

2. Use k you found and the x they gave you to find x

Ex 2. Y varies inversely as x, and y = -6 when x = 8.

Find y when x = 3

1. Write an equation that relates x & y.

k= -482. Find y when x= 3.

y= -16

68

k

x

ky

48y

x

48

3y

Solve the problem in two parts.

1. Use the inverse variation equation to find k when they give you both x and y

2. Use k you found and the x they gave you to find x