# Assume that y varies inversely as x, how do you write an inverse variation equation that relates x and y given y=8 when x=6?

Dec 13, 2017

$x y = 48$ is the inverse variation equation of $x \mathmr{and} y$

#### Explanation:

y prop 1/x :. y = k*1/x or x*y= k ; k is constant of

proportionality. y=8 ; x=6 ; x*y=k :. k = 6*8=48

$\therefore x \cdot y = 48$ is the inverse variation equation of $x \mathmr{and} y$ [Ans]

Dec 13, 2017

$y = \frac{48}{x}$

#### Explanation:

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

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

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

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

$y = 8 \text{ when } x = 6$

$y = \frac{k}{x} \Rightarrow k = y x = 8 \times 6 = 48$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{48}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$