algorithm - Finding an intersection between something and a line -

I have a set of numbers that is connected to an unknown method, or to be more accurate, the method is known but It can be one of several - it can be polynomial interpolation, stripe, simple linear ... - and a line, now think that it was given in simple form of y = ax + b .

For the interpolation, I do not know which method is used (i.e. the function is hidden ), so I can only determine y for some x And equally x

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its unknown The function is y = f (x) and the row is y = g (x) = ax + b . The intersection of these defects will be zero of Δy = f (x) -g (x) . Use just to find the roots of Δy - use the simplest.