# Suppose that y varies inversely with x, and y = 2 when x = 6. What is an equation for the inverse variation?

Apr 7, 2018

$y = \frac{12}{x}$

#### Explanation:

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

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

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

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

$y = 2 \text{ when } x = 6$

$y = \frac{k}{x} \Rightarrow k = y x = 6 \times 2 = 12$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{12}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$