# Assume y varies inversely as x, how do you write the equation given y=2 when x=20?

Jun 4, 2018

$y = \frac{40}{x}$

#### Explanation:

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

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

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

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

$y = 2 \text{ when } x = 20$

$y = \frac{k}{x} \Rightarrow k = y x = 2 \times 20 = 40$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{40}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$