# Assume that y varies inversely as x, how do you write an inverse variation equation that relates x and y given y=-1 when x=-12?

Jan 4, 2018

$y = \frac{12}{x}$

#### Explanation:

We know that $y \propto \frac{1}{x}$, and since $y$ is proportional to $\frac{1}{x}$ we can add a constant, $y = k \frac{1}{x}$.

To find $k$ we rearrange to get $k = y x$

We are given $x$ and $y$, so we just put our values in to get $k = x y = - 12 \cdot - 1 = 12$

$y = 12 \cdot \frac{1}{x} = \frac{12}{x}$

Jan 4, 2018

$y - \frac{12}{x}$

#### Explanation:

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

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

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

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

$y = - 1 \text{ when } x = - 12$

$y = \frac{k}{x} \Rightarrow k = y x = - 12 \times - 1 = 12$

$\text{equation is } \textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = \frac{12}{x}} \textcolor{w h i t e}{\frac{2}{2}} |}}}$