# If x varies inversely with y and x = 4 when y = 9, how do you find x when y = 6?

Apr 18, 2018

$x = 6$

#### Explanation:

$\text{the initial statement is } x \propto \frac{1}{y}$

$\text{to convert to an equation multiply by k the constant}$
$\text{of variation}$

$\Rightarrow x = k \times \frac{1}{y} = \frac{k}{y}$

$\text{to find k use the given condition}$

$x = 4 \text{ when } y = 9$

$x = \frac{k}{y} \Rightarrow k = x y = 4 \times 9 = 36$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{x = \frac{36}{y}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "y=6" then}$

$x = \frac{36}{6} = 6$