A teacher the city tried to boot for slapping a student not only get her job back, but deserves $85,000 in back-pay, a court ruled yesterday.

Former Brooklyn elementary-school teacher Beverly Riley spent two years in court battling her 2010 firing for striking a student who got too “sassy” for her liking, DOE documents say.

She was reinstated in January after an appeals court found that her punishment had been too harsh.

Yesterday, a Manhattan Supreme Court judge ruled she was entitled to a year’s back pay.