# What is the slope of a line perpendicular to x - 3y = 9?

Apr 11, 2015

Let $r$ and $s$ be to lines, and ${m}_{r}$ and ${m}_{s}$ their slopes. The two lines are perpendicular if the following relation holds:

${m}_{s} = - \frac{1}{m} _ r$

So, we must find the slope of the line $x - 3 y = 9$, and using the relation wrote above we'll find the perpendicular slope.

To find the slope of a line, we must manipulate its equation in order to bring it into the form

$y = m x + q$

and once in that form, $m$ will be the slope. Starting from $x - 3 y = 9$, we can add $3 y$ to both sides, obtaining $x = 3 y + 9$. Subtracting $9$ from both sides, we get $x - 9 = 3 y$. Finally, dividing by $3$ both sides, we have $y = \frac{1}{3} x - 3$.

Since our slope is $\frac{1}{3}$, its perpendicular slope will be $- 3$