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To solve for the slope of the line passing through the points \((4, -6)\) and \((-2, 3)\), we use the slope formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

### Step-by-Step Solution:
1. Assign the coordinates:
   - \((x_1, y_1) = (4, -6)\)
   - \((x_2, y_2) = (-2, 3)\)

2. Substitute into the formula:
   \[
   m = \frac{3 - (-6)}{-2 - 4}
   \]

3. Simplify:
   - Numerator: \(3 - (-6) = 3 + 6 = 9\)
   - Denominator: \(-2 - 4 = -6\)

   \[
   m = \frac{9}{-6}
   \]

4. Simplify further:
   \[
   m = -\frac{3}{2}
   \]

### Final Answer:
The slope of the line is:
\[
m = -\frac{3}{2}
\]

Would you like more details or have questions? Here are five follow-up concepts:

1. What does a slope of \(-\frac{3}{2}\) indicate about the line's direction?
2. How do we interpret slope in the context of rise over run?
3. Can you find the equation of this line in slope-intercept form?
4. How do we verify the slope using the distance formula?
5. What happens to the slope if the two points are swapped?

**Tip:** Always simplify fractions in slope calculations to avoid errors!

What is the slope of the line that passes through the points (4, -6) and (-2, 3)? Write your answer in simplest form.

Learn how to find the slope of a line passing through two points (4, -6) and (-2, 3). This problem covers algebraic concepts, specifically using the slope formula. Ideal for students in Grades 8-10.

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