Image of a line under a transformation (matrices)

The plane transformation $V$ is represented by the matrix $\begin{pmatrix} 1 & 4 \\2 & -1 \end{pmatrix}$ .

$L_1$ is the line with equation $y = 0.5x + k$ , and $L_2$ is the image of $L_1$ under $V$.

Find, in the form $y = mx + c$ , the cartesian equation for $L_2$ .


So far I have considered the general point of $y = 0.5x + k$ to be $\begin{pmatrix} t , & 0.5t + k \end{pmatrix}$.

So $\begin{pmatrix} 1 & 4 \\2 & -1 \end{pmatrix}$$\begin{pmatrix} t \\0.5t + k \end{pmatrix}$ $=$ $\begin{pmatrix} 3t + 4k \\1.5t - k \end{pmatrix}$

From here on I get a little stuck so could do with some assistance, thanks

So you equation
$\begin{pmatrix}x\\y\end{pmatrix}=\begin{pmatrix}4k\\-k\end{pmatrix}+t\begin{pmatrix}3\\1.5\end{pmatrix}$
Eliminate t.