The statement "
y varies inversely as
x means that when
x increases,
y decreases by the same factor. In other words, the expression
xy is constant:
where
k is the constant of variation.
We can also express the relationship between
x and
y as:
y =  |
|
where
k is the constant of variation.
Since
k is constant, we can find
k given any point by multiplying the x-coordinate by the y-coordinate. For example, if
y varies inversely as
x, and
x = 5 when
y = 2, then the constant of variation is
k = xy = 5(2) = 10. Thus, the equation describing this inverse variation is
xy = 10 or
y = 
.
Example 1: If
y varies inversely as
x, and
y = 6 when
x = 
, write an equation describing this inverse variation.
k =
(6) = 8 xy = 8 or
y =
Example 2: If
y varies inversely as
x, and the constant of variation is
k = 
, what is
y when
x = 10?
xy =
10y =
y =
×
=
×
=