# If y varies directly as x and y=3 when x= 2, find y when x=8?

May 15, 2018

$y = 12$

#### Explanation:

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

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

$\Rightarrow y = k x$

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

$y = 3 \text{ when } x = 2$

$y = k x \Rightarrow k = \frac{y}{x} = \frac{3}{2}$

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

$\text{when "x=8" then}$

$y = \frac{3}{\cancel{2}} ^ 1 \times {\cancel{8}}^{4} = 3 \times 4 = 12$

May 15, 2018

$y = 12$ when $x = 8$

#### Explanation:

Given : $y$ varies directly as $x$
$\therefore x \propto y$

$\implies x = k y$, where $k$ is constant of proportionality.

$\implies y = \frac{x}{k}$--------(1)

When $x = 2 , y = 3$

$\implies 2 = k \times 3$

$\implies k = \frac{2}{3}$

$\therefore$ when x =8, (1) $\implies y = \frac{8}{\frac{2}{3}}$

$\implies y = 8 \times \frac{3}{2} = 4 \times 3 = 12$

$y = 12$