To write the equation of the line that passes through the points $(2, 1)$ and $(-4, -8)$, we need to follow these steps:

1. Find the slope $m$:

The slope $m$ of the line passing through two points $(x_1, y_1)$ and $(x_2, y_2)$ is given by: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Substituting the given points $(x_1, y_1) = (2, 1)$ and $(x_2, y_2) = (-4, -8)$:

$m = \frac{-8 - 1}{-4 - 2} = \frac{-9}{-6} = \frac{3}{2}$

2. Write the equation in point-slope form:

The point-slope form of the equation of a line is: $y - y_1 = m(x - x_1)$ Using the slope $m = \frac{3}{2}$ and the point $(2, 1)$:

$y - 1 = \frac{3}{2}(x - 2)$

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

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. How do you convert the point-slope form to slope-intercept form?
2. What is the significance of the slope in a linear equation?
3. How do you find the x-intercept and y-intercept from the equation of a line?
4. What is the equation of a line parallel to this one passing through a different point?
5. How can you determine if two lines are perpendicular using their slopes?

Tip: Remember, the slope $m$ tells you how steep the line is and the direction it goes.