If the points $( x, y), (1, 2)$and $( -3, 4)$ are collinear, then 

If$(x, y), (1, 2)$ and $(-3, 4).$ are collinear then slope of line joining $(x, 4)$ and $(1, 2)$ is same as line joining points $(1, 2)$ and $( -3, 4)$or line joining $(x, 4)$ to $(-3, 4).$ 

So, $\frac{2-y}{1-x}=\frac{4-2}{-3-1}=\frac{4-y}{-3-x}$

$\begin{array}{r}\Rightarrow \frac{2-y}{1-x}=-\frac{1}{2}\Rightarrow \frac{y-2}{1-x}=\frac{1}{2}\\ \Rightarrow -4+2y=1-x\Rightarrow x+2y-5=0\end{array}$