# If y=-5 when x=3, how do you find x when y=-3 given that y varies inversely as x?

Aug 6, 2017

$x = 5$

#### Explanation:

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

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

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

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

$y = - 5 \text{ when } x = 3$

$y = \frac{k}{x} \Rightarrow k = y x = - 5 \times 3 = - 15$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{15}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } y = - 3$

$x = - \frac{15}{y} = - \frac{15}{- 3} = 5$