How to Level subfloor for hardwood
Another way it to just glue and screw/nail long timber packers over the existing joists (on top of the old flooring). Just follow the old nails/screws.

Rip down some 2" stock exactly the height of the dip. i.e. 1/8" on the first 3/16" on the second and so on until you're putting a 3/4" packer on the last joist. 

This assumes the new flooring is suitable for this configuration and is fixed at each joist and not bonded to the subfloor like parquet etc.