I have recently learned that there is much disagreement on the subject of reclining seats, with angry and vociferous groups protesting that either a) the airline makes the seats to recline, they've paid for their seat, and they should jolly well have the right to recline them whenever and for as long as they like, with the possible exception of during meals; and b) people who insist on reclining their seat, especially on short flights, are ignorant boors who have no consideration for others. There are sub-groups of the very short or very tall; the rich, who can afford to fly first-class where everyone has plenty of room to recline as they please; the obese; those who must work on their laptop computer for every minute of the flight; those with babies on their laps; and on and on. There are even devices sold that may be surreptitiously inserted into the seat in front of you to prevent it from reclining.
That said (!) "put my seat back" is fine, as is "recline my seat." "Person sitting in the back" usually means the last row or rows. "Sitting behind" needs an object for the preposition; "the person sitting behind me."
"Excuse me, but now that the flight attendants have turned off the lights, I'd like to recline my seat."
"I'm sorry, but as you can see I'm six foot four, and furthermore I'm working on an important presentation on my laptop computer while breastfeeding my infant. If you put your seat back, I will be extremely inconvenienced."
[not a teacher]