Question

What is the equation of a line that passes through the point (6, 1) and is perpendicular to the line whose equation is y=−2x−6y=−2x−6 ?

Answer 1

Lets get the negative reciprocal of the slope so we get
$m = \frac{1}{2}$
Now the equation that is perpendicular is
$y = \frac{1}{2} x + b$
Lets solve for b by plugging in the point (x,y)=(6,1)
$1 = \frac{1}{2} (6) + b \\ 1 = 3 + b \\ 1 - 3 = b \\ b = - 2$
Now plug that into the equation. So the equation of the line that is perpendicular and
passes through the point (6, 1) is
$y = \frac{1}{2} x - 2$