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 = (1)/(2)`
Now the equation that is perpendicular is

`y = (1)/(2) x + b`
Lets solve for b by plugging in the point (x,y)=(6,1)

`1 = (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 = (1)/(2) x - 2`