Ideally the plot will be horizontal until it reaches the proper voltage and then it will make a 90-degree turn and go straight up( indicating zero resistance.

Of course the vertical won't be vertical and the sharp 90 won't be absolutely sharp. Some are sharper than others and with smaller radius bends. We want to be operating in the near-vertical portion of the zone.
regards,
Douglas

look through Digi-Key or Mouser and download at least one LED data shet and see what is going on.