Question

A line is perpendicular to y = -x - 2
and intersects the point (-5,10).
What is the equation of this
perpendicular line?

Answer 1

Answer:

The equation of the perpendicular line will be:  $y=x+15$

Step-by-step explanation:

Given the equation of line

$y = -x - 2$

comparing with slope-intercept form

$y=mx+b$

so

The slope of the line is -1.

i.e. $m=-1$

As we know that perpendicular lines do have negative-reciprocal slopes.

so the slope of the line we need to find is 1.

i.e.

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

Plugging in the point (-5, 10) given into the equation

$y=mx+b$

$10=\left(1\right)\left(-5\right)+b$

$-5+b=10$

$b=15$

So the equation of this  perpendicular line will be

$y=mx+b$

$y=\left(1\right)x+15$

$y=x+15$

Therefore, the equation of the perpendicular line will be:  $y=x+15$