Let $$w_1, w_2, \dots, w_n$$ be complex numbers. A line $$L$$ in the complex plane is called a mean line for the points $$w_1, w_2, \dots, w_n$$ if $$L$$ contains points (complex numbers) $$z_1, z_2, \dots, z_n$$ such that $$\sum_{k = 1}^n (z_k-w_k) = 0.$$ For the numbers $$w_1 = 32 + 170i, w_2 = -7 + 64i, w_3 = -9 +200i, w_4 = 1 + 27i,$$ and $$w_5 = -14 + 43i$$, there is a unique mean line with y-intercept $$3$$. Find the slope of this mean line.

(第五届AIME1987 第11题)