Which of the following is an equation of the line that passes through the point (0, 0) and is perpendicular to the line shown above?(0,3),(5,-1)

Question

I dont under stand why the reciprocal waa uswd in finding the answer or the process that was used to get to it.

Answer 1

The slope of the line through (0,3) and (5,-1) is (-1-3) / (5-0) = -4/5

Any line perpendicular to the given line has slope -1 / (-4/5) = 5/4.

If the perpendicular line contains (0,0), then an equation of that line is y - 0 = (5/4) (x - 0)

So, y = (5/4)x