# Y varies inversely as X, and Y = 1/5 when X = 35, how do you find the variation constant and the equation of variation for the given situation?

May 14, 2017

$y = \frac{7}{x}$

#### Explanation:

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

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

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

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

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

$\text{when x= 35 } y = \frac{1}{5}$

$\Rightarrow k = \frac{1}{5} \times 35 = 7$

$\text{equation of variation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{7}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$