The problem asks for the slope-intercept form of the equation of a line that passes through the points $(-4, 3)$ and $(2, -9)$.

To find the equation, we first need to calculate the slope ($m$) using the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Given the points $(-4, 3)$ and $(2, -9)$, we can plug in the values:

$m = \frac{-9 - 3}{2 - (-4)} = \frac{-9 - 3}{2 + 4} = \frac{-12}{6} = -2$

So the slope ($m$) is $-2$.

Now, we'll use the slope-intercept form of the line equation:

$y = mx + b$

We can plug in one of the points (I'll use $(2, -9)$) and the slope $m = -2$ to solve for $b$ (the y-intercept):

$-9 = -2(2) + b$ $-9 = -4 + b$ $b = -9 + 4 = -5$

Now that we have the slope $m = -2$ and the y-intercept $b = -5$, the equation of the line is:

$y = -2x - 5$

Would you like more details on any of the steps? Here are 5 questions to extend your understanding:

1. How do you find the equation of a line given two points?
2. Why do we need to calculate the slope first?
3. What does the slope-intercept form represent geometrically?
4. How can you use another point to check the equation of the line?
5. What happens if two points have the same x-coordinate or y-coordinate?

Tip: Always double-check the sign when subtracting coordinates, as small mistakes can affect the slope calculation.