# If y varies directly as x and y = -24 when x = 8, then how do you find y when x = 10?

Mar 30, 2018

$y = - 30$

#### Explanation:

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

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

$\Rightarrow y = k x$

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

$y = - 24 \text{ when } x = 8$

$y = k x \Rightarrow k = \frac{y}{x} = \frac{- 24}{8} = - 3$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = - 3 x} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when "x=10" then}$

$y = - 3 \times 10 = - 30$