# How do I write the equation of a line that is perpendicular to y=3x+4 and goes through the point (3,5)?

Nov 21, 2015

$y = - \frac{1}{3} x + 6$

#### Explanation:

Two perpendicular lines have opposite reciprocal slopes.

The slope in $y = 3 x + 4$ is $3$, so the line perpendicular to it will have a slope of $- \frac{1}{3}$.

We can write this in the form $y = - \frac{1}{3} x + b$ and then plug in $\left(3 , 5\right)$ for $x$ and $y$ to find the equation of the line perpendicular to the line $y = 3 x + 4$ that goes through the point $\left(3 , 5\right)$.

$5 = - \frac{1}{3} \left(3\right) + b$
$5 = - 1 + b$
$6 = b$

Therefore, the equation of our new line is: $y = - \frac{1}{3} x + 6$.