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A set of points on a straight line are called 'collinear points'.
A straight line is the shortest distance between two points, a line is the delineation of a connection between two or more points.
Yes. Consider the drawing of a table. ~ Actually, a circle is the set of all points at a given distance from the center. It's technically not derived from a line.
The shortest distance between two points is... a straight line.
In coordinated geometry the points on a straight line will determine its equation.