Given that triangle $\displaystyle ABC$ has points, $\displaystyle A(8,2), B(0,6),$ and $\displaystyle C(-3,2)$, point $\displaystyle C$ can be moved along a certain line with points $\displaystyle A$ and $\displaystyle B$ remaining stationary, and the area of Δ$\displaystyle ABC$ will not change. What is the slope of that line?

(It says the answer in my book which is $\displaystyle -\frac {1}{2}$)