To find the equation of the line passing through the points $(-3, -7)$ and $(9, 1)$, we first need to calculate the slope of the line using the slope formula:

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

Substitute the given points $(-3, -7)$ and $(9, 1)$ into the formula:

$m = \frac{1 - (-7)}{9 - (-3)} = \frac{1 + 7}{9 + 3} = \frac{8}{12} = \frac{2}{3}$

Now that we have the slope $m = \frac{2}{3}$, we use the point-slope form of the equation of a line:

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

We can use either point. Let's use $(-3, -7)$:

$y - (-7) = \frac{2}{3}(x - (-3))$

Simplifying:

$y + 7 = \frac{2}{3}(x + 3)$

Thus, the equation of the line in point-slope form is:

$y + 7 = \frac{2}{3}(x + 3)$

Let me know if you'd like further details or explanations!

Here are 5 related questions to explore:

1. How can you convert this equation to slope-intercept form?
2. What is the equation if we use the point $(9, 1)$ instead?
3. How do we find the x-intercept of this line?
4. Can this equation be expressed in standard form?
5. What happens if the slope between two points is zero?

Tip: The point-slope form is very useful when you know one point and the slope of a line—it allows you to write the equation quickly without needing the y-intercept!