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

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

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

Step 1: Calculate the Slope ($m$)

The formula for 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 $(-2, -8)$ and $(8, 8)$ into this formula:

$m = \frac{8 - (-8)}{8 - (-2)} = \frac{8 + 8}{8 + 2} = \frac{16}{10} = 1.6$

Step 2: Apply the Point-Slope Formula

Using the point-slope form $y - y_1 = m(x - x_1)$, we can choose either point. Let's use $(-2, -8)$:

$y - (-8) = 1.6(x - (-2))$

Simplify:

$y + 8 = 1.6(x + 2)$

This is the equation of the line in point-slope form.

Would you like more details, or have any questions?

Here are 5 related questions to practice:

1. What is the equation of the line passing through $(3, 4)$ and $(7, 12)$?
2. How do you convert a point-slope equation to slope-intercept form?
3. What is the equation of a vertical line passing through $(5, -3)$?
4. If a line has a slope of 2 and passes through the point $(1, -1)$, what is its equation?
5. How do you find the slope of a line parallel to the line passing through $(6, 2)$ and $(9, 8)$?

Tip: When writing equations in point-slope form, you can use any of the given points. Just make sure to calculate the slope correctly!