The zero of a function is a point where the function evaluates to zero. If you express "y" as a function of "x", i.e. y = f(x), then for a zero of the function, the y-coordinate is 0. In other words, the corresponding point is on the x-axis.
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the very center of a coordinate plane is called the origin or (0,0) :D
All points in a plane do have a y-coordinate. Its value may be 'zero' ... if the point happens to lie on the x-axis ... but 'zero' is a perfectly good coordinate.If you want all points whose y-coordinate is not zero, then those are |y| > 0. (Absolute value of 'y' is greater than zero.)
coordinate plane
All points with a 0 for the x coordinate is the y axis.
Yes, x,0,z is on the y=0 plane