# How do you write an equation of the line perpendicular to the line x - 3y = 9 and passing through the point (3,5)?

Jul 4, 2015

I found: $y = - 3 x + 14$

#### Explanation:

Your perpendicular line musta have a slope ${m}_{1}$ given as:
${m}_{1} = - \frac{1}{m}$ where $m$ is the slope of your given line.
Your line can be written as:
$y = \frac{x}{3} - 3$
The slope of your given line is equal to the numerical coefficient of $x$, i.e., $m = \frac{1}{3}$.
With this in mind the slope of the perpendicular will be: ${m}_{1} = - 3$.
We can now use the general relatonship:
$y - {y}_{0} = {m}_{1} \left(x - {x}_{0}\right)$ to find the equation of the perpendicuar line;
$y - 5 = - 3 \left(x - 3\right)$
$y = - 3 x + 9 + 5$
$y = - 3 x + 14$