Question

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

The line through that point and the origin has a slope of -1. It is perpendicular to the line you want, so the line you want has slope +1. Its equation can be written as
.. y = (x -4) -4
or, in standard form
.. x - y = 8