1988 AIME Problem 11

Let w_{1}, w_{2}, \ldots, w_{n} be complex numbers. A line L in the complex plane is called a mean line for the points w_{1}, w_{2}, \ldots, w_{n} if L contains points (complex numbers) z_{1}, z_{2}, \ldots, z_{n} such that


For the numbers w_{1}=32+170 i, w_{2}=-7+64 i, w_{3}=-9+200 i, w_{4}=1+27 i, and w_{5}=-14+43 i there is a unique mean line with y-intercept 3 . Find the slope of this mean line.