Suppose you have a plane like 3x-12y+5z=30.
The intercepts then are (4,0,0), (0,6m0), (0,0,3)
So we plot them to get a triangular region, but does that mean this plane has a finite region or does it continue on forever?
Words mean things. Don't magically assign new meanings because you have some additional information.
A plane is an infinite region.
Intercepts are points in the plane.
Intercepts do NOT define the limits fo the plane.
The triangular region is contained in the plane.
Ok, got that part now.
One more question....
does it matter which axis you call x, y, and z if you are making a 2D representation of a 3D coordinate system? I've seen most places make the z axis pointing outwards, but since you can rotate, can you label the axes arbitrarily?