# If y varies inversely with x and y = 8 when x = 5, then what is y when x = 2?

Apr 29, 2017

$y = 20$

#### Explanation:

"varies inversely means " 1/("variable")

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

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

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

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

$\text{that is " y=8" when } x = 5$

$y = \frac{k}{x} \Rightarrow k = x y = 5 \times 8 = 40$

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

$\text{when } x = 2 \to y = \frac{40}{2} = 20$