To find the equation of the line that passes through the points $(2, -8)$ and $(-2, 0)$, we follow these steps:

Step 1: Find the slope of the line

The slope $m$ of a line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by the formula:

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

Substitute the points $(2, -8)$ and $(-2, 0)$:

$m = \frac{0 - (-8)}{-2 - 2} = \frac{0 + 8}{-4} = \frac{8}{-4} = -2$

So, the slope of the line is $m = -2$.

Step 2: Use point-slope form

The point-slope form of a line is:

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

We can use one of the points, say $(2, -8)$, and the slope $m = -2$:

$y - (-8) = -2(x - 2)$

Simplify the equation:

$y + 8 = -2(x - 2)$ $y + 8 = -2x + 4$ $y = -2x + 4 - 8$ $y = -2x - 4$

Final equation

The equation of the line is:

$y = -2x - 4$

Let me know if you want further details or have any questions! Here are some related questions you can explore:

1. What is the y-intercept of the line $y = -2x - 4$?
2. How do you convert the slope-intercept form to standard form?
3. What is the distance between the two points $(2, -8)$ and $(-2, 0)$?
4. What is the equation of a line parallel to $y = -2x - 4$ passing through $(1, 3)$?
5. What is the equation of a line perpendicular to $y = -2x - 4$?

Tip: When finding the slope between two points, remember to subtract the coordinates in the correct order to avoid sign errors.