Suppose let us take two physical quantities x and y.Assume that they have a physical relationship.Give any value to x say x1 and obtain the value for y as y1.Give another value for x say x2 and obtain the value of y as y2, through the physical relationship you have.If you find that the ratio of x1 and x2 equals the ratio of y1 and y2, then it means that the given physical relationship is linear..