# Assume y varies inversely as x, how do you write the equation given y=12 when x=-9?

Nov 17, 2017

$y = - \frac{108}{x}$

#### Explanation:

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

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

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

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

$y = 12 \text{ when } x = - 9$

$y = \frac{k}{x} \Rightarrow k = y x = 12 \times - 9 = - 108$

$\text{the equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - \frac{108}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$