To determine how many points lie on the y-axis, we need to look for the ordered pairs where \( x = 0 \) since the y-axis is defined by all points where the x-coordinate is 0.
From the table of ordered pairs given:
\[ \begin{array}{c|c} x & y \ \hline -7 & 4 \ -3 & 0 \ 0 & 2 \ 1 & 6 \ 5 & 0 \ 9 & -2 \ \end{array} \]
We can see that there is only one ordered pair where \( x = 0 \), which is \( (0, 2) \).
Since there is only one point on the y-axis, the answer is 1.