"What do all members of the family of linear functions

f(x) = c - x

have in common?"

Answer in the back of the book is "The slope is -1"

I think I understand that, but...is there any particular reason it is written as f(x) = c - x instead of f(x) = c - mx? I'm guessing "m" is just implied or something, I don't know.

Also I don't really know what it means by "family" of linear functions.