Question 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
$$
\sum_{k=1}^n(z_k-w_k)=0.
$$
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.
$$
\sum_{k=1}^n(z_k-w_k)=0.
$$
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.