Question

Line perpendicular to the line that goes through (0,0) and (3,2)

Answer 1

Since the first line passes thru the origin, you can read off its slope from the coordinates of the other point (3,2):  the slope is m = 2/3.

A line perpendicular to the first has slope -3/2, the negative reciprocal of 2/3.

Thus, the perpendicular line is    y = (-3/2)x + b.  Subbing 0 for y and 0 for x, we get b = 0.  Therefore, the equation of this new line is y = (-3/2)x.