# If y varies inversely as x, and y = 18 when x = 2, how do you find y when x = 4?

May 21, 2018

y = 9

#### Explanation:

If x is doubled then y is cut in half, since they are inversely related

$\frac{18}{2} = 9$

May 21, 2018

$y = 9$

#### Explanation:

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

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

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

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

$y = 18 \text{ when } x = 2$

$y = \frac{k}{x} \Rightarrow k = y x = 18 \times 2 = 36$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{36}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "x=4" then}$

$y = \frac{36}{4} = 9$