Given that the linear transformation $\displaystyle \left(\begin{array}{cc} x' \\ y' \end{array} \right) = \left(\begin{array}{cc} 3 & 2 \\ 1 & 4\end{array} \right)\left(\begin{array}{cc} x \\ y \end{array} \right)$ moves point $\displaystyle (x,y)$ to point $\displaystyle (x',y')$, determine m such that a point on the line $\displaystyle y=mx$ moves to the line $\displaystyle y=mx$

I don't get this sentence.

Determine m such that a point on the line $\displaystyle y=mx$ moves to the line $\displaystyle y=mx$

move to the same line???