Plotting a constant y-axis plane

I am trying to plot a plane such that the y-axis is constant at 3 on a 3-D graph. So the plane is going to be stick upwards parrellel to x-axis while staying at y=3 throughout. The idea is to actually have this plane to cut another surface. I try to get the function in the form of z=f(x,y) and here's what I did:

Since the plane is a constant y=3 plane, I assume (0, 3, 0) is a point on the plane. Then I move 5 in the z-axis and then minus them to get a vector direction.

I then get another vector direction on this plane by moving 2steps up z-axis and 5 steps to x-axis; (2, 3, 5).

Then I cross these 2 direction vectors to get the normal line.

I then did a dot product of this normal vector with the point (0, 3, 0) to get the equation of the plane:

But, from , how do I form it to z=f(x, y)? z is zero in this case and I can't make it the subject in terms of x and y.

How should I carry on from here? Thanks.