# If y varies inversely with x, and x = -12 when y = 5. How do you find the inverse variation equation and use it to find the value of x when y = 10?

Sep 13, 2017

$y = - \frac{60}{x} , x = - 6$

#### Explanation:

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

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

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

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

$x = - 12 \text{ when } y = 5$

$y = \frac{k}{x} \Rightarrow k = x y = - 12 \times 5 = - 60$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{60}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } y = 10$

$x = - \frac{60}{y} = - \frac{60}{10} = - 6$