# What is an equation of the line that passes through the point (-9,5) and is perpendicular to the line whose equation is y=1/2x+5?

Dec 25, 2016

$y = - 2 x - 13$

#### Explanation:

Perpendicular lines $L$ and $L '$ with slopes $m$ and $m '$, respectively, have the following property with the slopes

$m = - \frac{1}{m}$

In case the slope is 0, the slope of the perpendicular line would be undefined, and vice versa. This would mean you are dealing with horizontal/vertical lines.

Given the line $L : y = \frac{1}{2} x + 5$, we have

$m = \frac{1}{2}$

Which means the line $L '$ which is perpendicular to $L$ has the following slope

$m ' = - \frac{1}{\frac{1}{2}}$

$\implies m ' = - 2$

Now that we know the slope of $L '$, let's find its y-intercept.

$L ' : y = - 2 x + b$

To find the y-intercept, let's insert the point which we know lies on the line $L '$.

$p ' : \left(- 9 , 5\right)$

$\implies L ' : 5 = - 2 \left(- 9\right) + b$

$\implies - 13 = b$

Therefore, the equation of the line $L '$ which is perpendicular to $L$ and passes through the point $\left(- 9 , 5\right)$ is

$y = - 2 x - 13$