To find the y-value when \( x = 13 \) for the function \( y = \frac{1}{2}\sqrt{x + 3} - 9 \), we can substitute \( x \) with 13:
\[ y = \frac{1}{2}\sqrt{13 + 3} - 9 \]
First, calculate \( 13 + 3 \):
\[ 13 + 3 = 16 \]
Now take the square root:
\[ \sqrt{16} = 4 \]
Now substitute back into the equation for \( y \):
\[ y = \frac{1}{2} \cdot 4 - 9 \]
Calculate \( \frac{1}{2} \cdot 4 \):
\[ \frac{1}{2} \cdot 4 = 2 \]
Now subtract 9:
\[ y = 2 - 9 = -7 \]
So, when \( x = 13 \), the y-value is \( -7 \).
Therefore, the answer is:
\(-7\).