For what value of $k$ are the points $(1, 3)$, $(2, 5)$ and $(4, k)$ collinear?

Explanation

1. 01

   Three points are collinear when the triangle they make has area 0, so the determinant is 0.

2. 02

   $\begin{vmatrix}1 & 3 & 1 \\ 2 & 5 & 1 \\ 4 & k & 1\end{vmatrix} = k - 9 = 0$ gives $k = 9$.