To find the equation of the line passing through the points $(-8, -3)$ and $(-7, 0)$, we'll first use the point-slope form of a line equation:

$y - y_1 = m(x - x_1)$

where $m$ is the slope, and $(x_1, y_1)$ is a point on the line.

Step 1: Find the slope ($m$) using the slope formula:

$m = \frac{y_2 - y_1}{x_2 - x_1}$ Substitute the points $(-8, -3)$ and $(-7, 0)$:

$m = \frac{0 - (-3)}{-7 - (-8)} = \frac{0 + 3}{-7 + 8} = \frac{3}{1} = 3$

Step 2: Use the point-slope form.

We can now substitute $m = 3$ and one of the points, say $(-8, -3)$, into the point-slope form:

$y - (-3) = 3(x - (-8))$

Simplify:

$y + 3 = 3(x + 8)$

This is the fully simplified point-slope form of the line equation.

Would you like more details, or do you have any other questions?

Here are 5 related questions for practice:

1. Write the equation of the line passing through the points $(2, 5)$ and $(4, 9)$.
2. Find the slope of the line passing through $(0, 0)$ and $(3, 7)$.
3. Convert the equation $y + 1 = 2(x - 3)$ to slope-intercept form.
4. What is the equation of a horizontal line passing through $(4, 7)$?
5. Determine if the points $(1, 2)$ and $(1, -3)$ form a vertical line.

Tip: The point-slope form is especially useful when you know the slope and one point on the line.