How can I approach this problem?
You certainly need to add at least one other variable representing the time of year, because from your graph it's clear that the fare can't be predicted accurately using only the time until departure: for the same day you can have many points representing different fares. That makes sense, since the fares are going to be very different depending if the flight occurs during holiday season or not. There might also be other variables of interest but since it's always the same flight I can't think of any.

I would suggest plotting a graph where x is the time of year and the time before departure is represented for instance with colour or gradient, that should make things clearer.