# How do you write an inverse variation equation given y=2 when x=5?

Jul 30, 2017

$y = \frac{10}{x}$

#### Explanation:

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

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

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

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

$y = 2 \text{ when } x = 5$

$y = \frac{k}{x} \Rightarrow k = x y = 5 \times 2 = 10$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{10}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$