# How do you write an equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5)?

Jul 20, 2015

I found: $y = - 5 x + 15$

#### Explanation:

I would use the relationship:
$y - {y}_{0} = m \left(x - {x}_{0}\right)$
Where $m$ is the slope and ${x}_{0} , {y}_{0}$ are the coordinates of your point.
The slope $m$ of the perpendicular is given as: $m = - \frac{1}{m} _ 1$ where ${m}_{1}$ is the slope of your given line:
Your line can be written (isolating $y$):
$y = \frac{x}{5} + 2$ which has slope ${m}_{1} = \frac{1}{5}$ (the coefficient of $x$).
So, the slope of the perpendicular will be:
$m = - 5$
Finally you get:
$y - 5 = - 5 \left(x - 2\right)$
$y = - 5 x + 10 + 5$
$y = - 5 x + 15$