All lines are defined by two or more distinct points.
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No. Two distinct points define a single line.
You cannot define a line with a single point (a single point only defines itself). You need two points to define a line (and therefore to write the equation for it).
It will have end points to be a distinct line segment
No, 2 points define a line, 3 points define a plane.
They define one plane. A line is defined by two points, and it takes three points to define a plane, so two points on the line, and one more point not on the line equals one plane.