# Is 1/x+3y=-5 a linear function and explain your reasoning?

Jan 16, 2017

This is not a linear function. Explanation below.

#### Explanation:

We can modify the expression, so it has $y$ alone on one side:

$3 y = - \frac{1}{x} - 5 \implies y = - \frac{1}{3} \frac{1}{x} - 15$.

We can see that this is basically the hyperbola $y = - \frac{1}{3} \frac{1}{x}$

shifted 15 units downwards, and hyperbolas are not linear functions.