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Consider the affine transformation \(f(P)=\begin{bmatrix}1 & 2 \\3 & 4\end{bmatrix}P+\begin{bmatrix}5\\6\end{bmatrix}\).

Find the image of \(ax+by+c=0\) under \(f\).

My answer is \(\left(a-\frac{b}{2}\right)y+\left(\frac{3b}{2} -2a\right)x+4a-\frac{9b}{2}+c=0\).

Find the image of \(ax+by+c=0\) under \(f\).

My answer is \(\left(a-\frac{b}{2}\right)y+\left(\frac{3b}{2} -2a\right)x+4a-\frac{9b}{2}+c=0\).

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