The question in the image asks for the value of $q$ corresponding to point $D(-4, q)$, which is on a line in a coordinate plane along with other points: $A(-2, 3)$, $B(4, -1)$, and $C(4, 4)$.

To solve for $q$, we can analyze the line that passes through $A(-2, 3)$ and $D(-4, q)$.

1. Find the slope of the line through $A$ and $D$: The slope $m$ of a line through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $A(-2, 3)$ and $D(-4, q)$ into this formula, we have: $m = \frac{q - 3}{-4 - (-2)} = \frac{q - 3}{-2}$

2. Check the slope of the line through $B(4, -1)$ and $C(4, 4)$: This line is vertical (both points share the same x-coordinate, $x = 4$), so it does not affect the calculation of $q$.

Next, assuming the configuration of the image suggests we need to balance between other directions (or some external guidance for checking slopes in a different fashion), we'd check the options (like $q = -6$).

Is there a specific formula method that