graph $3\\mathbf{w}$ with its initial point at the initial point of $\\mathbf{w}$.

Explanation:

Step1: Identify initial and terminal points of $\mathbf{w}$

The initial point is $(-9, -7)$ and the terminal point is $(-3, -3)$.

Step2: Calculate the components of vector $\mathbf{w}$

$$ \mathbf{w} = \langle -3 - (-9), -3 - (-7) \rangle = \langle 6, 4 \rangle $$

Step3: Calculate the components of vector $3\mathbf{w}$

$$ 3\mathbf{w} = 3 \langle 6, 4 \rangle = \langle 18, 12 \rangle $$

Step4: Determine the terminal point of $3\mathbf{w}$

Starting at $(-9, -7)$, the terminal point is $(-9 + 18, -7 + 12) = (9, 5)$.

Answer:

To graph $3\mathbf{w}$, draw a vector starting at the initial point $(-9, -7)$ and ending at the terminal point $(9, 5)$.