1. A line passes through $(k,-9)$ and $(7,3 k)$ and has slope $2 k$. Find the possible values of $k$.
Answer: $\frac{9}{2}$ or 1
Solution: We have $\frac{3 k-(-9)}{7-k}=2 k$, so $3 k+9=2 k(7-k)$ or $2 k^{2}-11 k+9=(2 k-9)(k-1)=0$. Hence $k=\frac{9}{2}$ or $k=1$.