The problem asks for the equation of the line passing through the points $(-5, -8)$ and $(-1, -6)$ in point-slope form.

Steps:

1. Find the slope: The slope $m$ between two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting $(-5, -8)$ as $(x_1, y_1)$ and $(-1, -6)$ as $(x_2, y_2)$: $m = \frac{-6 - (-8)}{-1 - (-5)} = \frac{-6 + 8}{-1 + 5} = \frac{2}{4} = \frac{1}{2}$

2. Use point-slope form: The point-slope form of a line is: $y - y_1 = m(x - x_1)$ Using the slope $m = \frac{1}{2}$ and one of the points, say $(-5, -8)$: $y - (-8) = \frac{1}{2}(x - (-5))$ Simplifying: $y + 8 = \frac{1}{2}(x + 5)$

Final equation in point-slope form:

$y + 8 = \frac{1}{2}(x + 5)$

You do not need to simplify further.

Would you like further clarification or additional details? Here are some related questions you might find interesting:

1. How do you convert point-slope form to slope-intercept form?
2. What are the other forms of a linear equation?
3. Can you derive the equation of the line using a different point from the pair?
4. How would you find the equation of the line if you were given a slope and one point?
5. How does the point-slope form compare to the general form of a line?

Tip: Always double-check the slope calculation to ensure accuracy when working with two points.