#
Section 3-3

#
Direct and Inverse Variation

Direct variation
describes a simple relationship between two variables. We say
*
y
*
**
varies directly
**
**
with
**
*
x
*
(or
*
as x
*
, in some textbooks) if:

*
***
y
**
**
=
***
k
*
*
x
*

for some constant
*
k
*
.

The graph of the direct variation equation is a straight line through the origin.

Direct Variation Equation

for 3 different values of
*
k
*

Inverse variation
describes another kind of relationship. We say
*
y
*
**
varies inversely
**
**
with
**
*
x
*
(or
*
as x
*
, in some textbooks) if
*
:
*

*
***
xy
**
**
=
***
k
*
,

or, equivalently,

for some constant
*
k
*
.

The graph of the inverse variation equation is a hyperbola.

Inverse Variation Equation

for 3 different values of
*
k
*