To find the slope of the line that contains the points \((2, -8)\) and \((-4, 4)\), we can use the formula for the slope \(m\) between two points \((x_1, y_1)\) and \((x_2, y_2)\):
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Let \((x_1, y_1) = (2, -8)\) and \((x_2, y_2) = (-4, 4)\). Plugging in the values:
\[ m = \frac{4 - (-8)}{-4 - 2} \]
Now simplify:
\[ m = \frac{4 + 8}{-4 - 2} = \frac{12}{-6} = -2 \]
Thus, the slope of the line is \(-2\).