To find the equation of the line that passes through the points $(-4, 2)$ and $(-8, -2)$, we can use the point-slope form of the equation of a line:

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

First, we need to calculate the slope $m$ using the formula:

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

Substituting the coordinates $(-4, 2)$ as $(x_1, y_1)$ and $(-8, -2)$ as $(x_2, y_2)$:

$m = \frac{-2 - 2}{-8 - (-4)} = \frac{-4}{-4} = 1$

Now that we have the slope $m = 1$, we can use the point-slope form. Let's use the point $(-4, 2)$ for $(x_1, y_1)$:

$y - 2 = 1(x - (-4))$

Simplifying:

$y - 2 = x + 4$

Adding 2 to both sides to get the equation in slope-intercept form $y = mx + b$:

$y = x + 6$

So, the equation of the line that passes through the points $(-4, 2)$ and $(-8, -2)$ is:

$y = x + 6$

Would you like more details on any step? Here are some related questions:

1. How do you find the slope if you have different coordinates?
2. What is the point-slope form of a line equation?
3. How can you convert between different forms of linear equations?
4. What is the importance of the slope in a linear equation?
5. How can you check if a point lies on a given line?

Tip: To verify your result, you can substitute the coordinates of both points into the final equation to ensure they satisfy it.