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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.

Write a slope-intercept equation for a line that passes through the points (-4, 3) and (2, -9).

Learn how to write the slope-intercept equation of a line that passes through the points (-4, 3) and (2, -9). This problem covers key algebraic concepts like finding the slope using two points and deriving the equation of the line in slope-intercept form.

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