# If y=4 when x=14, how do you find x when y=-5 given y varies inversely as x?

Jun 1, 2017

$x = - \frac{56}{5}$

#### Explanation:

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

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

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

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

$y = 4 \text{ when } x = 14$

$y = \frac{k}{x} \Rightarrow k = x y = 14 \times 4 = 56$

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{56}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}} \leftarrow \text{ is the equation}$

$\text{when } y = - 5$

$- 5 = \frac{56}{x} \Rightarrow x = - \frac{56}{5}$