when i plotted x+y=z in xyz plane i got a straight line.what do i infer from this
Sorry, but the text of your question doesn't make sense ...
The given equation describes a plane which passes through the origin and it's normal vector is .
And the intersection of this plane with one of the coordinate planes (xy, xz or yz) is a straight line. Therefore the given plane isn't parallel to any of the three coordinate planes.
But as I mentioned above there isn't a xyz plane.