# If y varies inversely as x. When y = 12, x = 7. How do you find the constant of variation and use it to determine the value for y when x = 4?

Mar 24, 2016

The constant of variation is $84$
When $x = 4$ then $y = 21$

#### Explanation:

If $y$ varies inversely as $x$ then
$\textcolor{w h i t e}{\text{XXX}} x y = c$ for some constant of variation $c$

We are told $\left(x , y\right) = \left(7 , 12\right)$ is a solution for this equation so
$\textcolor{w h i t e}{\text{XXX}} 7 \times 12 = c$
$\Rightarrow$$\textcolor{w h i t e}{\text{XXX}} c = 84$

When $x = 4$
$\textcolor{w h i t e}{\text{XXX}} 4 y = 84$
$\Rightarrow$$\textcolor{w h i t e}{\text{XXX}} y = 21$