# How do you decide whether the relation xy+7y=7 defines a function?

Nov 9, 2015

You can rearrange the expression to find that $y$ is uniquely determined in terms of $x$, therefore a function.

#### Explanation:

$7 = x y + 7 y = \left(x + 7\right) y$

Notice that if $x = - 7$ then there are no solutions, since this results in $7 = 0 y = 0$.

If $x \ne - 7$ then we can divide both sides by $x + 7$ to get:

$\frac{7}{x + 7} = y$

That is:

$y = \frac{7}{x + 7}$

This uniquely determines the value of $y$ for any value of $x$ apart from $x = - 7$, where it is not defined.