To find the equation of the line that passes through the points (-2, 7) and (3, -8), we first need to calculate the slope (m) using the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let's assign the points as follows:
- \((x_1, y_1) = (-2, 7)\)
- \((x_2, y_2) = (3, -8)\)
Now, substitute the values into the slope formula:
\[ m = \frac{-8 - 7}{3 - (-2)} = \frac{-15}{3 + 2} = \frac{-15}{5} = -3 \]
Now that we have the slope \( m = -3 \), we can use the point-slope form of the line's equation, which is given by:
\[ y - y_1 = m(x - x_1) \]
Using the point (-2, 7):
\[ y - 7 = -3(x - (-2)) \]
This simplifies to:
\[ y - 7 = -3(x + 2) \]
Expanding the right side:
\[ y - 7 = -3x - 6 \]
Now, add 7 to both sides to isolate \( y \):
\[ y = -3x - 6 + 7 \] \[ y = -3x + 1 \]
Thus, the equation of the line in slope-intercept form \( (y = mx + b) \) is:
\[ \boxed{y = -3x + 1} \]