There are three criterias to determine the linearity of a system:
(assuming y is the output and x is the input)
1- if y = f(x) then a*y = f(a*x)
2- if y1 = f(x1) and y2 = f(x2) then y1 + y2 = f(x1 + x2)
3- if x = 0 then y=f(0) = 0
If a system can satisfy the criterias above, it is linear, but sometimes, proving such thing needs creativity.
So to answer to your question I have to say there is a rule but checking the rule might not be so straight forward sometimes.