Back was also accused of giving the girl gifts, and when she was in hospital at one point, he was seen cuddling her and holding her hand.
He also failed to report worrying incidents to do with her mental health, including her cutting herself and asking him to "save me".
Mepham's serious misconduct relates to those events.
Back apologised to the girl's family at the hearing.
"I know that saying sorry isn't enough. I tried my best to keep [the girl] safe and to convince her to re-connect with you so you can work it all out together because that's what family is about. I never ever spoke disrespectfully and disparagingly about you to [the girl]," he said.
"In hindsight, I can say that I lost my way and became too involved in a student's life," he said.
The girl's mother gave evidence to the tribunal, saying she noticed a change in her once-popular, outgoing and sporty daughter.
After the mother became aware of the relationship, she said, her daughter was reluctant to talk about it and get the male teacher in trouble.
"From our perspective as parents it showed a relationship that was inappropriate... This all came as a complete shock to us," the mother said.
"We consider [the male teacher's] behaviour went well beyond what we would expect as parents in a teacher/student relationship. He was dishonest and lied to us."
The coroner is investigating the girl's death.