1. The problem asks for the equation of a line passing through the point $(7, -9)$ with an undefined slope. 2. An undefined slope means the line is vertical. 3. The equation of a vertical line passing through $x = a$ is simply $x = a$. 4. Since the line passes through $(7, -9)$, the equation is $x = 7$. 5. This matches option A. Final answer: $x = 7$