Consider the line parametrized by
\(x = 2t+1 \)
\(y=-3t+2\)
Find a vector \(\begin{pmatrix}a\\b\end{pmatrix}\) that's parallel to this line and satisfies \(a+b=3\).
\(v = \alpha\begin{pmatrix}2\\-3\end{pmatrix},~\alpha \in \mathbb{R}\\ 2\alpha - 3\alpha = 3\\ \alpha = -3\\ v = \begin{pmatrix}-6\\9\end{pmatrix}\)
