I was thinking about some ideas and I was wondering if there is a way to make a dynamic line of pixels for the fishing rod, especially if the player wants to move when the bait is set the line should stretch, but I don't really know how.

If you instead know how to obtain that effect but only in a 3D environment, feel free to share your knowledge too.

I use Unity.

I think the only way is using some number of objects and bind them with the hinge joints

I mean, I just used the LineRenderer. With these two lines of code:

link.GetComponent<LineRenderer>().SetPosition(0, transform.position);

link.GetComponent<LineRenderer>().SetPosition(1, target.position);

(though, I don't know if this would work in 3d.)