what teacher did voldermort kill at the start? i cant make it out x\

If you mean the muggle studies teacher in the beginning of DH, her name was Charity Burbage.

Charity Burbage, shes the muggle studies teacher.

Charity Burbage. She taught Muggle Studies at Hogwarts before she was captured and killed by Voldemort. We don't really hear much about her, so that may be the reason you couldn't make it out.