Linear equations have the highest exponent of the variable equal to 1.
4+y= 2x linear
2x^2+x-5 = y non linear ( exponent 2)
y= x/2-4 linear
2x+7y= 9 linear
y-2 = 2 (x-3) linear
y=2^x non linear
3/x+9 = y non linear ( it has asymptotes)