Question

Precalc question, please help?

The point nearest to the origin on a line is at (4, -4). Find the standard form of the equation of the line.

Answer 1

I know that the answer is x-y-8=0, I just don't know how to find that.

Answer 2

The closest approach point (4, -4) lies on a line that is perpendicular to the line you have already. That means it has a slope which is -1/m
compared with the slope m of the line you have.

Get the new line's slope from change in y / change in x, from the
(4,-4) point to the origin (0,0)

(-4 - 0)/(4-0) = -1

The slope of your original line is thus -1/(-1) = m = 1

y = (1) x + b

-4 = 4 + b so b = -8

y = x - 8, which is what you know the answer to be.

Answer 3

Thank you!