# If y varies inversely as x, and y = 5 as x = 6, how do you find y for the x-value of 10?

Jun 11, 2018

$y = 3$

#### Explanation:

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

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

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

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

$y = 5 \text{ when } x = 6$

$y = \frac{k}{x} \Rightarrow k = y x = 5 \times 6 = 30$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{30}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "x=10" then}$

$y = \frac{30}{10} = 3$