Need help creating a filter interface in JSUI / V8UI
Since I am a complete novice in programming, I decided to ask you for help.
Here is a reference to the filter I would like to get.

My thoughts: most likely, this is not a Band Pass filter, but two cutoff filters with adaptive Slope (from 12 to 48 dB/Octave). Moving up sets the distance between the bands and the filter slope, while moving horizontally sets the frequency. The amplitude range on the graph is from (unknown) to ~+6 dB.
If anyone can help me with this, I would be very grateful! Thank you!
(saw your shelving question last week and was not sure what to say about it.
the actual design/implementation of poles and zeroes filter kernels is a contentious subject, some people would prefer to use [cascade~], which allows you to optimize for CPU similar to how you would design multipole filters in C++, other would say that to learn about filters it will be better to stack basic modules consiting of individual biquads serially.
the filtermode 7 in modern versions of max / filtergraph~ is convenient but at the same time can be quite confusing about what happens.
the simplest version of a shelving has no Q - and only up to 3 db/oct and if you desing things like that they will look quite different.)
now specifically for this question here:
i would split the job into various parts.
1. generate the coefficients
2. display the accumulated result
3. make the mouse input do what you want it to do to 1. and 2.

you probably want to use a butterworth with no Q (or Q set to fixed 1.) and not filtergraphs lowpass/highpass mode; if you dont want to calculate this filter type yourself, filterdesign has it ready for you, including higher order.
for the mouse control, don´t miss out that GUI objects can be made transparent and/or disallow to be clicked on.