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)