Are f (x) = 3x - 10 and 2x + 7y = 28 both functions, if not which one isn't and why?

Both are functions. Try not to get tripped up on notation of functions. They are they same, just written differently.

f (x) = 3x-10 is the same as 0=3x-10

2x+7y=28 is the same as 2x+7y-28=0

Just one will give you a line and the other will give you a circle. If you are ever unsure, plug them into a graphing calculator and see what you get back.