To find the positive value of \( y \) when \( x = 9 \) in the equation \( y^2 - x = 7 \), we start by substituting \( x \) with 9.
The equation becomes:
\[ y^2 - 9 = 7 \]
Next, we can solve for \( y^2 \):
\[ y^2 = 7 + 9 \] \[ y^2 = 16 \]
Now, we take the square root of both sides to find \( y \):
\[ y = \sqrt{16} \]
This gives us:
\[ y = 4 \quad \text{or} \quad y = -4 \]
Since we are looking for the positive value of \( y \), we take:
\[ y = 4 \]
Thus, the positive value of \( y \) when \( x = 9 \) is
\[ \boxed{4} \]