Determine homogeneous transformation matrix for reflection about the line $y = mx + b$, or specifically $y = 2x - 6$ 
Determine the homogeneous transformation matrix for reflection about the line
$y = mx + b$,  or specifically $ y = 2x - 6$.

I use  $mx - y +b =0$:  $\text{slope} = m$,  $\tan(\theta)= m$
intersection with the axes:
$x =0$  is $y = -b$   and  $y =0$ is  $x = \dfrac{b}{m}$
My question is, what  can I do next?

Note that any matrix $\mathbf A\cdot \vec{0}=\vec{0}$, so there is no matrix that can flip over $y=2x-6$ as it must map $\vec 0 \to (4 \frac{4}{5},-2\frac{2}{5})$.  You might want to do something about that.
