# If y varies inversely as x and y = 8 when x = 4, find y when x = 16?

Mar 22, 2017

$y = 2$

#### Explanation:

The statement is expressed as $y \propto \frac{1}{x}$

$\text{inverse means " 1/"variable}$

To convert to an equation introduce k, the constant of variation.

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

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

To find k use the given condition that y = 8 when x = 4

$8 = \frac{k}{4} \Rightarrow k = 4 \times 8 = 32$

$\Rightarrow \text{ equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{32}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$x = 16 \to y = \frac{32}{16}$

$\Rightarrow y = 2 \text{ when } x = 16$