# Suppose that y varies inversely with x. How do you use the information to find k, and then choose the equation given x=25 and when y=5?

Jul 12, 2017

$y = \frac{125}{x}$

#### Explanation:

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

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

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

$\text{to find k use the given condition for x and y}$

$x = 25 \text{ when } y = 5$

$y = \frac{k}{x} \Rightarrow k = x y = 25 \times 5 = 125$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{125}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$