How to adjust the length of a line passing through a point?

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@Cornel wrote:

 

My desire: 

Having a point, for example: (x, F(x)) = (1,1), I would like to be able to adjust the LENGTH of the line passing through that point (1,1), in order the length of the line to be smaller or larger as shown below. How could I do this?

 

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Simply plot the line segment by providing the coordinates of the two end points:

Of course you also could provide a range for the abscissa values to limit the line