2.  Remember: x and y show direct variation
if y = kx for some nonzero constant k.
 Variables x and y show inverse variation
if:
k is called the constant of variation
 y is said to “vary inversely” with x

3.  Totell whether x and y show direct or
inverse variation:
1. Rewrite by solving for y
2. Check which pattern it follows
Examples:

4.  Dox and y show direct variation,
inverse variation, or neither?

5.  Use given values of x and y to find k.
 Then, write equation using form.
 Example:
 The variables x and y vary inversely, and
y = 8 when x = 3.
 Write an equation that relates x and y.
 Find y when x = -4.

6. x and y vary inversely, and y = 6 when
x = 1.5.
 Write an equation that relates x and y.
 Find y when x = 4/3

7.  The inverse variation equation can be
rewritten as xy = k.
 A set of data pairs (x, y) vary inversely if
the products xy are approximately
constant.
Example: Does the data show inverse
variation? If so, write a model relating x
and y.
x 3.6 5.0 6.3 4.0 2.8
y 32.5 23.5 18.7 29.2 42.2

8.  Do these data show inverse
variation? If so, find a model.
w 2 4 6 8 10
h 9 4.5 3 2.25 1.8

9.  When a quantity varies directly as the
product of two or more other quantities
it is joint variation.
 If z = kxy where k ≠ 0, then z “varies
jointly” with x and y.

10.  Write an equation for each given
relationship.
a. y varies directly with x
b. y varies inversely with x
c. z varies jointly with x and y
d. y varies inversely with the square of x
e. z varies directly with y and inversely with x