For what value of $k$ are the points $(k, 2)$, $(3, 4)$ and $(5, 6)$ collinear?

Explanation

1. 01

   Collinear points make $\begin{vmatrix} k & 2 & 1 \\ 3 & 4 & 1 \\ 5 & 6 & 1 \end{vmatrix} = 0$.

2. 02

   Expanding: $k(4 - 6) - 2(3 - 5) + (18 - 20) = -2k + 2 = 0$, so $k = 1$.