# How do you write an inverse variation equations given y=4 when x =7?

Jan 19, 2016

$x y = 28$

#### Explanation:

An inverse variation is of the form:
$\textcolor{w h i t e}{\text{XXX}} x y = c$ for some constant $c$.

For the equation $x y = 28$

$\textcolor{w h i t e}{\text{XXX}} y = 4$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = 7$

If we multiply the value of $y$ by $2$ (for example)
$\textcolor{w h i t e}{\text{XXX}} y = 8$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x = \frac{7}{2}$
That is multiplying $y$ by $2$ results in the need to divide $x$ by $2$;
which is the basic concept of inverse variation.