To find the equation of the line passing through the points $(-6, -9)$ and $(-3, 9)$, we need to first calculate the slope of the line and then use the point-slope form of the equation of a line.

Step 1: Calculate the slope $m$

The formula to find the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is:

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

Substitute the points $(-6, -9)$ and $(-3, 9)$:

$m = \frac{9 - (-9)}{-3 - (-6)} = \frac{9 + 9}{-3 + 6} = \frac{18}{3} = 6$

So, the slope $m = 6$.

Step 2: Use the point-slope form of the equation

The point-slope form of a line is:

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

We can use either of the two given points $(-6, -9)$ or $(-3, 9)$. Let's use the point $(-6, -9)$:

$y - (-9) = 6(x - (-6))$

Simplify:

$y + 9 = 6(x + 6)$

Final Answer:

The equation of the line in point-slope form is:

$y + 9 = 6(x + 6)$

Would you like more details on how this form works or need clarification on any step?

Here are some related questions:

1. How do you convert point-slope form to slope-intercept form?
2. How do you find the equation of a line when given just the slope and one point?
3. What is the general equation of a line in standard form?
4. How would you find the equation of a line parallel or perpendicular to another?
5. How do you calculate the distance between two points on a line?

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