##### Task7

What shape is the set of solutions \(\left(\begin{smallmatrix} x \\ y \end{smallmatrix}\right)\) to the equation\begin{equation*} \begin{pmatrix} 3 \\ 7\end{pmatrix} \cdot \begin{pmatrix} x \\ y \end{pmatrix} = 5? \end{equation*}

That is, if we look at all possible vectors \(\left(\begin{smallmatrix} x \\ y \end{smallmatrix}\right)\) which make the equation true, what shape does this make in the plane?

What happens if we change the vector \(\left(\begin{smallmatrix} 3 \\ 7 \end{smallmatrix}\right)\) to some other vector? What happens if we change the number \(5\) to some other number?