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!