Question 105589
 
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:
                                                   {{{xy = k}}}
where {{{k}}} is the constant of variation.

We can also express the relationship between {{{x}}} and {{{y}}} as:

{{{y = k/x}}} where {{{k}}} is the constant of variation.


Unlike the graph of direct variation, the graph of inverse variation is {{{not}}}{{{ linear}}}. Rather, it is a {{{hyperbola}}}.

To graph an inverse variation, make a data table and plot points. Then connect the points with a smooth (not straight) curve. There should be two curves -- one in the first quadrant (where both {{{x}}} and {{{y}}} are positive) and one in the third quadrant (where both {{{x}}} and {{{y}}} are negative).