How can I know how to interpret the output coefficients (`coefs_`) from the model sklearn.svm.LinearSVC()?
Here's one (admittedly hard) way.

If you really want to understand the low-level details, you can always work through the source code. For example, we can see that the LinearSVC fit method calls _fit_liblinear. That calls train_wrap in liblinear, which gets everything ready to call into the C++ function train.

So train in linear.cpp is where the heavy lifting begins. Note that the w member of the model struct in the train function gets mapped back to coef_ in Python.

Once you understand exactly what the underlying train function does, it should be clear exactly what coef_ means and why we draw the lines that way. 

While this can be a little laborious, once you get used to doing things this way, you will really understand how everything works from top to bottom.