To find the slope of the line given by the equation \(-48 = 2x - 8y\), we can rearrange it into the slope-intercept form, which is \(y = mx + b\), where \(m\) is the slope.
Starting with the given equation:
\[ -48 = 2x - 8y \]
We can isolate \(y\). First, move the \(2x\) to the left side:
\[ -48 - 2x = -8y \]
Next, divide every term by \(-8\) to solve for \(y\):
\[ y = \frac{-48}{-8} + \frac{-2x}{-8} \]
This simplifies to:
\[ y = 6 + \frac{1}{4}x \]
Now we can see that the equation is in the form \(y = mx + b\), where \(m = \frac{1}{4}\) is the slope.
Thus, the slope of the line is
\[ \boxed{\frac{1}{4}} \]