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Space is a boundless, three dimensional set of all points. Collinear is a set of points that are all on the same line and is 3 or more points.
A series of 3 points will always determine a plane unless 2 or all 3 points are identical points (they have the same coordinates).If the idea is to have the three points determine oneplane, a unique plane, then three points will do that as long as none of them have the same spacial coordinates (have identical locations) or as long as the three points do not lie on a single line.If a straight line can be drawn through all three points, they will not form one unique plane either.
3 coplanar points may or may not be collinear. 3 collinear points must be coplanar.
Points: (2,-5) and (3, -3) Slope: (-3 - -5)/(3-2) = 2
Points: (4, 6) and (12, 3) Slope: -3/8