To answer this adequately, you'll need to find the slope of each of the four given line segments. I note that the slope of the fourth one, NP, is
-6 + 3 -3 m = ----------- = ----- 2 - 0 2
This slope is the same as that of the given line, and therefore these 2 lines are parallel, not perpendicular. So eliminate the fourth possibility and concentrate on the other 3 until you find the one that has slope +2/3. Reminder: perpendicular lines are characterized by negative reciprocal slopes.
The first equation will turn into -18x -6y = -18, and the second equation will turn into 14x + 6y = 18. The y terms will cancel out when you add the equations together.
