# Are these two lines parallel, perpendicular, or neither? Explain. 9x+3y=8, 3x+9y=8

Nov 24, 2015

The given lines are neither parallel nor perpendicular.

#### Explanation:

To check if two lines are parallel or perpendicular it is good to change the equations to form $y = a x + b$

The first line is:

$9 x + 3 y = 8$

$3 y = - 9 x + 8$

$y = - 3 x + \frac{8}{3}$

The second line is:

$3 x + 9 y = 8$

$9 y = - 3 x + 8$

$y = - \frac{1}{3} x + \frac{8}{9}$

From those equations we can see that those lines are neither parallel nor perpendicular

They would be parallel if the coefficients of $x$ were equal.

They would be perpendicular if the coefficients of $x$ were inverse and opposite numbers (for example $3$ and $\left(- \frac{1}{3}\right)$ or $\left(- 2\right)$ and $\frac{1}{2}$)