f(x) = mx +b, if m!=0, we can say f(x) and x are linearly related.

f(x)=mx is linear. But I don't think f(x)=mx+b is linear because of the additional b. For example: f(ax) = max+b != a(mx+b) = amx + ab

I think f(x)=mx+b, when b=0 it's linear; when b!=0 it's affine