To find the slope ($m$) of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$, we use the formula:

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

For the points $(-4, -6)$ and $(-8, -12)$:

1. Let $(x_1, y_1) = (-4, -6)$
2. Let $(x_2, y_2) = (-8, -12)$

Now, substitute these values into the slope formula:

$m = \frac{-12 - (-6)}{-8 - (-4)}$

Simplify the expressions in the numerator and the denominator:

$m = \frac{-12 + 6}{-8 + 4} = \frac{-6}{-4} = \frac{3}{2}$

Thus, the slope of the line passing through the points $(-4, -6)$ and $(-8, -12)$ is:

$m = \frac{3}{2}$

Would you like more details on this calculation or have any questions?

Here are some related questions to deepen your understanding:

1. How do you interpret the slope of $\frac{3}{2}$ in terms of rise and run?
2. What would the line equation look like if we use the point-slope form for these points?
3. How would the slope change if the points were flipped in order?
4. Can you determine if the line is increasing or decreasing based on the slope?
5. What would the slope be if the line were vertical?

Tip: The slope of a line can give you a quick sense of its steepness and direction. A positive slope means the line rises as it moves to the right, while a negative slope means it falls.