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The purpose of a line plot is usually to see each frequency of the numbers.
Its so its easy to caculate
Line can go forever. It is always straight
The purpose is to easily convey the slope of a line and a point it passes through in algebraic form. With these two pieces of information it is possible to map a line in in 2D space.
The purpose of hidden lines is to represent edges that are not directly visible. The purpose of center lines is to represent the axes of circular features.