To find the slope \( m \) of the line passing through the points \((x_1, y_1)\) and \((x_2, y_2)\), we use the formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
For the points \((3, 8)\) and \((7, -7)\), we have:
- \(x_1 = 3\), \(y_1 = 8\)
- \(x_2 = 7\), \(y_2 = -7\)
Substituting these values into the slope formula gives:
\[ m = \frac{-7 - 8}{7 - 3} \]
Calculating the numerator:
\[ -7 - 8 = -15 \]
Calculating the denominator:
\[ 7 - 3 = 4 \]
Now, substituting these results into the slope formula:
\[ m = \frac{-15}{4} \]
Thus, the slope of the line passing through the points \((3, 8)\) and \((7, -7)\) is
\[ \boxed{-\frac{15}{4}}. \]