To find the value of the function \( y = \frac{1}{8}x - 13 \) when \( x = -4 \), we can substitute \( -4 \) for \( x \) in the equation:
\[ y = \frac{1}{8}(-4) - 13 \]
Calculating \( \frac{1}{8}(-4) \):
\[ \frac{1}{8}(-4) = -\frac{4}{8} = -\frac{1}{2} \]
Now, substituting back into the equation:
\[ y = -\frac{1}{2} - 13 \]
Converting \( -13 \) to a fraction with the same denominator:
\[ -13 = -\frac{26}{2} \]
Therefore:
\[ y = -\frac{1}{2} - \frac{26}{2} = -\frac{1 + 26}{2} = -\frac{27}{2} \]
Now, converting \( -\frac{27}{2} \) to a decimal gives us:
\[ -\frac{27}{2} = -13.5 \]
Thus, the value of the function when \( x = -4 \) is \( -13.5 \).
So the answer is A. -13.5.