# If y varies inversely as x and y = -3 when x = 6, how do you find x when y is 36?

Apr 26, 2017

$x = - \frac{1}{2}$

#### Explanation:

$\textcolor{b l u e}{\text{Inverse"" means " 1/"variable}}$

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

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

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

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

$y = - 3 \text{ when } x = 6$

$y = \frac{k}{x} \Rightarrow k = x y = 6 \times - 3 = - 18$

$\text{the equation is } y = \frac{- 18}{x}$

$\text{to find x when y = 36}$

$y = \frac{- 18}{x} \Rightarrow x = \frac{- 18}{y}$

$\Rightarrow x = \frac{- 18}{36} = - \frac{1}{2}$