It is possible.
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The x and y axes intersect at the point of origin at (0, 0) on the Cartesian plane
It is the point of origin (0, 0) where the x and y axes meet at right angles on the Cartesian plane
Yes, except when the line is in the plane. In the latter case, they intersect at each point on the line (an infinite number).
If the line is not IN the plane ... it just zaps through the plane from some direction ... then it touches the plane in only one point. The intersection is a point.if it is lined up with the plane, then the intersection is a line.
The axes of coordinate planes intersect at the point of origin.