Let $\mathbf{v}$ be the vector from initial point $P_{1}$ to terminal point $P_{2}$. Write $v$ in terms of $\mathbf{i}$ and $\mathbf{j}$.
\[
P_{1}=(-2,9), P_{2}=(-6,3)
\]
$v=\square$ (Type your answer in terms of $i$ and $j$. )

Step 1 ：Let's denote the initial point as \(P_{1}=(-2,9)\) and the terminal point as \(P_{2}=(-6,3)\).

Step 2 ：We are looking for the vector \(\mathbf{v}\) from \(P_{1}\) to \(P_{2}\).

Step 3 ：The x-component of the vector is given by the difference in the x-coordinates of \(P_{2}\) and \(P_{1}\), and the y-component of the vector is given by the difference in the y-coordinates of \(P_{2}\) and \(P_{1}\).

Step 4 ：Calculating the x-component, we get \(v_{i} = P_{2}[0] - P_{1}[0] = -6 - (-2) = -4\).

Step 5 ：Calculating the y-component, we get \(v_{j} = P_{2}[1] - P_{1}[1] = 3 - 9 = -6\).

Step 6 ：Therefore, the vector \(\mathbf{v}\) can be written in terms of \(\mathbf{i}\) and \(\mathbf{j}\) as \(-4\mathbf{i} - 6\mathbf{j}\).

Step 7 ：Final Answer: \(v = \boxed{-4\mathbf{i} - 6\mathbf{j}}\)