Show that if two RVs X and Y are such that Y = aX +b then rhoXY is either 1, −1 or 0 depending on whether a is non-zero, and the sign of a. In other words, linearly related random variables (where a is not 0) will have a correlation coefficient which is 1 or −1. Note you can conclude that if two random variables have a correlation which is not ±1 then they are not in a linear relationship.