It is easily verified that the graphs of y = 1.1^x and y = x have two points of intersection, and the graphs of y = 2^x and y = x have no points of intersection. It follows that for some real number 1 < p < 2, the graphs of y = p^x and y = x have exactly one point of intersection. Using analytical and/or graphical methods, determine p and the coordinates of the single point of intersection.