If the results of the simpler ticket work out, AND we want more robust results, we can do the following:
To make the analysis more robust, we probably want to take into account both the x and y errors. To do that, you need "total least squares" or "orthogonal least squares" regression. There's an implementation in scipy here, but the API is pretty low-level, which means it's harder to work with.
https://docs.scipy.org/doc/scipy/reference/odr.html