# How do you find the equation of the line that passes through ( -2 , 7 ) and is PERPENDICULAR to x + 5y = 7?

Oct 1, 2015

I found: $y = 5 x + 17$

#### Explanation:

I would use the general form of the equation as:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
where:
$m =$slope
${x}_{0} , {y}_{0}$ are the coordinates of your point.
Now, to be perpendicular to your line $m$ must be equal to $- \frac{1}{m '}$ where $m '$ is the slope of your given line.
Your line can be written as:
$y = - \frac{1}{5} x + 75$ (isolating $y$);
with $m ' = - \frac{1}{5}$
and so:
$m = 5$
using this and your coordinates you have:
$y - 7 = 5 \left(x + 2\right)$
$y = 5 x + 10 + 7$
$\textcolor{red}{y = 5 x + 17}$