I would think a basic graphic equalizer could function as such: a bank of filters, each with their own connection through a potentiometer to a summer (such as an op-amp summer). However, I've run across several designs and it appears that while indeed it seems the boost is summed in this manner, the cut is also negatively summed at the input (for instance, here).
For reference, consider the following from the link, above:
Why would one do this? Why do we have to or would we want to "sum" the cut at all?
I get in theory, if I'm correct, the cut is feedback, inverted to the input op-amp (U1B in the link above), and so cancels some of that frequency.
Is this necessary, or a feature? Why is the boost summed to the output op-amp (U2A) instead of say the same opamp as the cut?
My apologies if I don't understand this design, it's one of the things I'd really like to make as a project.