To find the equation of the line passing through the points $(-3, -4)$ and $(1, 8)$, we can use the point-slope form of the equation of a line. The point-slope form is given by:

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

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

First, let's calculate the slope $m$ using the formula:

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

Substituting the given points $(-3, -4)$ and $(1, 8)$:

$m = \frac{8 - (-4)}{1 - (-3)} = \frac{8 + 4}{1 + 3} = \frac{12}{4} = 3$

So, the slope $m$ is 3.

Next, we'll use the point-slope form with one of the points. Let's use the point $(1, 8)$:

$y - 8 = 3(x - 1)$

Now, we'll simplify this equation to get the slope-intercept form $y = mx + b$:

$y - 8 = 3x - 3$ $y = 3x - 3 + 8$ $y = 3x + 5$

Therefore, the equation of the line passing through the points $(-3, -4)$ and $(1, 8)$ is:

$y = 3x + 5$

Would you like more details or have any questions?

Here are 5 related questions you might want to ask:

1. How do you find the equation of a line given its slope and a point on the line?
2. What is the general form of the equation of a line?
3. How do you convert from point-slope form to slope-intercept form?
4. How can you determine if two lines are parallel?
5. What is the formula for finding the distance between a point and a line?

Tip: When finding the equation of a line, ensure to calculate the slope accurately and choose the correct form of the equation (point-slope, slope-intercept, or general form) for your needs.