To find the equation of the line that passes through the points (3, -8) and (6, -4), we'll first need to calculate the slope (m) of the line using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Using the points (3, -8) and (6, -4):
- \( (x_1, y_1) = (3, -8) \)
- \( (x_2, y_2) = (6, -4) \)
Now, substituting these values into the slope formula:
\[ m = \frac{-4 - (-8)}{6 - 3} = \frac{-4 + 8}{3} = \frac{4}{3} \]
Now that we have the slope, we can use the point-slope form of the equation of a line, which is given by:
\[ y - y_1 = m(x - x_1) \]
Substituting in one of the points (let's use (3, -8)) and the slope \( m = \frac{4}{3} \):
\[ y - (-8) = \frac{4}{3}(x - 3) \]
This simplifies to:
\[ y + 8 = \frac{4}{3}(x - 3) \]
To isolate \( y \), we subtract 8 from both sides:
\[ y = \frac{4}{3}(x - 3) - 8 \]
Now, we need to simplify the equation further:
- Distribute \( \frac{4}{3} \):
\[ y = \frac{4}{3}x - \frac{4}{3} \cdot 3 - 8 \] \[ y = \frac{4}{3}x - 4 - 8 \]
- Combine like terms:
\[ y = \frac{4}{3}x - 12 \]
Thus, the equation of the line in slope-intercept form is:
\[ \boxed{y = \frac{4}{3}x - 12} \]