If Y varies inversely as twice x. When x = 3, y = 6 what is the value of y when x = 9?

Jan 2, 2018

$y = 2$

Explanation:

If $y$ is inversely proportional to $2 x$, therefore $2 x \cdot y = k$ for some constant $k$

When, $x = 3$, $y = 6$, $\therefore k = 36$

$\therefore 2 x y = 36$

When $x = 9$, $y = \frac{36}{2 x} = \frac{36}{18} = 2$

$\therefore y = 2$ when $x = 9$

Jan 2, 2018

$y = 2$

Explanation:

$\text{the initial statement is } y \propto \frac{1}{2 x}$

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

$\Rightarrow y = k \times \frac{1}{2 x} = \frac{k}{2 x}$

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

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

$y = \frac{k}{2 x} \Rightarrow k = 2 x y = 2 \times 3 \times 6 = 36$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{36}{2 x} = \frac{18}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{when } x = 9$

$\Rightarrow y = \frac{18}{9} = 2$