To find the constant of variation \( k \) in a direct variation graph, we can use the formula \( y = kx \). We can find \( k \) by using one of the given points (either \( (4, 1) \) or \( (-8, -2) \)).
Using the point \( (4, 1) \):
\[ 1 = k \cdot 4 \]
To solve for \( k \):
\[ k = \frac{1}{4} \]
Now we can check the second point \( (-8, -2) \) to ensure consistency:
\[ -2 = k \cdot (-8) \] \[ -2 = \frac{1}{4} \cdot (-8) \] \[ -2 = -2 \]
This confirms that both points satisfy the equation with \( k = \frac{1}{4} \).
Thus, the constant of variation is:
D) \( \frac{1}{4} \)