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

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.