How to find the coordinates of one coordinate system to another given straight line?

For example, there are two Cartesian coordinate systems, and there is a direct equation which we know in both these systems. How to find the relative position of coordinate systems (i.e., for example, the coordinates of the origin of the second system to the first, and the angle of rotation)?

P. S. an Interesting case of the plane and space.
March 19th 20 at 09:02
1 answer
March 19th 20 at 09:04
For simplicity, consider a special case: the line passes through the origin and in the 1st and in the 2nd system, the rotated system is the same. It turns out that the equation of the straight line in the two systems coincide, and the shift between systems can be anything. I.e. it is impossible to clearly determine solutions is infinite.

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