Chapter 8.10Inverse Variation

An inverse variation is a function defined by an

equation of the form

, where k is a nonzero constant.

or

You can say that y varies inversely as x or that y is

inversely proportional to x.

The con

xy k

ky

x

stant is called the constant of variation.k

The graph of an inverse variation is not a straight line, since the equation is not linear. The term xy is of degree 2.

xy k

Graph the equation 1xy Example 1

x y

-4 - ¼

-2 - ½

-1 -1

- ½ -2

- ¼ -4

x y

¼ 4

½ 2

1 1

2 ½

4 ¼

4

2

-2

-4

• The graph of an inverse variation is called a hyperbola (you WILL see these later in Algebra II)

• When k is positive, the branches are in Quadrants I and III.

• When k is negative, the branches are in Quadrants II and IV.

• Remember when you were a kid and tried to balance a teeter-totter (see-saw – a simple lever)?

• This is an example of an inverse variation• The heavier kid had to sit closer to the

middle of the teeter-totter to balance the lighter weight kid

• The equation that explains this phenomenon is

1 1 2 2m d m d

1 1 2 2

2

2

2

2

If a 24 g mass is 30 cm from the fulcrum of a lever, how far from the

fulcrum is a 45 g mass that balances the 24 g mass?

Use

24 30 45

720 45

720

4516

m d m d

d

d

d

d

Example 2

Summary of Variation Equations

Direct Variation Inverse Variation

1 2

1 2

y kx

yk

xy y

x x

1 1 2 2

ky

xxy k

y x y x