Well, you need several 3D lines so that the fishing line can curve etc.
Usually, the most direct method would be to have an array of 3D positions that try and stay within a fixed distance from the previous position in the array. So, the first position would be the end of the rod, then the second position maybe a foot of line. Then each loop, you update the array positions depending on their velocity, then again to constrain them to a fixed distance. Add in gravity to the first calculation and believe it or not - you'll have a reasonable string simulation, especially if it's balanced right.
With those rules, you could add in that any position that's under the water gets it's velocity reduced by a great amount, otherwise the velocity is reduced slowly. With that, it should be possible to tighten and slacken the line just by moving the rod, letting the line sink etc.
I've gotten some nice results with this technique in 2D, I'll see if I can make time to come up with an example.

I got a fever, and the only prescription, is more memes.
