# Assume that y varies inversely as x. If x = 12 when y = 9, what is x when y = -3?

Oct 4, 2016

$x = - 36$

#### Explanation:

The basic inverse variation equation is

$x y = k$

where $k$ is the constant of variation. In order to write the equation that reflects this relationship, we must find $k$. We use the known relationship of $x = 12$ and $y = 9$ to find $k$. Substituting in the basic equation, we will find $k$:

$x y = k$

$\left(12\right) \left(9\right) = k$

$108 = k$

This then yields the equation which relates $x$ and $y$:

$x y = 108$

Now, use this equation and substitute the second value of $y$ in order to find its related value of $x$:

$x y = 108$

$x \left(- 3\right) = 108$

$x = \frac{108}{- 3}$

$x = - 36$