To find the slope of the line passing through the points \(( -4, 1 )\) and \(( 4, -1 )\), you can use the slope formula:
\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]
Here, \((x_1, y_1) = (-4, 1)\) and \((x_2, y_2) = (4, -1)\).
Substituting the values into the formula:
\[ m = \frac{-1 - 1}{4 - (-4)} = \frac{-2}{4 + 4} = \frac{-2}{8} = \frac{-1}{4} \]
Therefore, the slope of the line is \(-\frac{1}{4}\).