# If y varies inversely as x and y = 20 when x = 10, then how do you find the constant of the variation?

May 17, 2016

constant of variation: $200$

#### Explanation:

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

Given $\textcolor{red}{y} = \textcolor{red}{20}$ when $\textcolor{b l u e}{x} = \textcolor{b l u e}{10}$ is a solution to this equation
then
$\textcolor{w h i t e}{\text{XXX}} \textcolor{b l u e}{10} \cdot \textcolor{red}{20} = c$

$\Rightarrow c = \textcolor{g r e e n}{200}$