Question

how can I tell my function f(x)=6x+2 is a legitimate function?

Answer 1

f(x) is just a substitute for symbol y. In other words, you have y=6x+2

That is just a line.

Answer 2

so how would I write that in complete sentences

Answer 3

I am not good at drawing, so
http://www.wolframalpha.com/input/?i=y%3D6x%2B2+from+-10+to+10

Answer 4

This part, the complete sentences is on you. Once you know what a function is, you can explain it. Exercising your English is good for you :)

Let me know if you need help.