a plane
Line.
a straight line
a line a ray goes in only one direction forever No, a line goes on forever in two directions, a ray starts at one point and then goes on forever.
An idealised line.
a plane
A plane
It is a plane.
Plane
Plane
You are probably looking for the word 'plane'.
plane
An endless flat surface, also known as an infinite plane, is a theoretical concept in geometry that extends indefinitely in all directions. It has the properties of being flat, meaning that at any point on the plane, the surface is perfectly level with no curvature. In mathematics, an infinite plane is often used as a simplified model for understanding concepts such as coordinate systems, vectors, and geometric shapes.
It is a plane.
There is no real world flat surface which goes on forever. It is a geometric idealised concept. So, since there is not even a first such thing, there cannot be another.
Line.
A flat surface, like a sheet of paper, with no edges (ie: it goes on and on and on and on....) or boundaries. What you're describing is a 2 dimensional plane. No, not plane like an airplane. A plane is simply a flat "sheet" that goes on forever in 2 dimensions: left/right (wide) and up/down (tall).