# If y varies inversely as x, and y = 2/5 when x = 2, how do you find y when x = 1?

Mar 28, 2018

$y = \frac{4}{5}$

#### Explanation:

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

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

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

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

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

$y = \frac{k}{x} \Rightarrow k = y x = \frac{2}{5} \times 2 = \frac{4}{5}$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{4}{5 x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } x = 1 \Rightarrow y = \frac{4}{5 \times 1} = \frac{4}{5}$