# Write an equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5)

Nathanial Levine 2022-09-29 Answered
Write an equation of the line perpendicular to the line x - 5y = -10 and passing through the point (2,5)
You can still ask an expert for help

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

Ricky Lamb
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:
$y-5=-5\left(x-2\right)$
$y=-5x+10+5$
$y=-5x+15$