Step 1: Think in terms of distance from each axis.
For any point $(x, y)$, the distance from the y-axis equals $|x|$ and the distance from the x-axis equals $|y|$. A point sits exactly on the y-axis when its distance from that axis is zero, meaning $x = 0$.
Step 2: Apply this to (0, -7).
Here $x = 0$, so the point is at zero distance from the y-axis, it sits right on it. The value $y = -7$ just tells us it is 7 units below the origin, along that same axis.
Step 3: Conclude.
Since the point lies exactly on an axis, it cannot belong to any quadrant either. \[ \boxed{\text{On the Y-Axis}} \]