Show that is linear of slope m if and only if (x + h) (x)

Show that ƒ is linear of slope m if and only if ƒ(x + h) − ƒ(x) = mh (for all x and h).

That is to say, prove the following two statements:

(a) ƒ is linear of slope m implies that ƒ(x + h) − ƒ(x) = mh (for all x and h).

(b) ƒ (x + h) − ƒ(x) = mh (for all x and h) implies that ƒ is linear of slope m.