Checking whether the system is linear or non linear
Depending on the system equation behavior of the curve of input versus output can be of any shape.

System is said to be linear if it satisfies these two conditions:


Superposition - if input applied is (x1+x2),  then the output obtained will be y1+y2 .(equivalently we say that if x1 and x2 are applied simultaneously then out put will be the sum of the outputs obtained individually)
Homogenity - if  (k * x1) input is applied, then output obtained will be k * y1. Here k is any real number.


Reference by this site