There exists one plane through any three noncollinear points. Since the points cannot be on the same line, at least two lines would have to pass through any of the three points.
Although theoretically there are infinite lines in space and in a plane, too, at least three non collinear points are necessary to define a plane. Two intersecting lines will therefore be necessary to define it (two points create a line); these intersecting lines are the ones to help define coordinates (x,y).
