If you were going to graphically determine the enthalpy of vaporization, δhvap, for this liquid, what points would you plot

It depends on what type of graph you have. The easiest would be using a H-T diagram. Enthalpy of vaporization is the physical change from liquid to vapor. It occurs at a constant pressure and a constant temperature. As shown in the picture, 1 point is drawn on the subcooled liquid, and another point of the saturated vapor isothermal line. Now, the difference between those two points is the value for the enthalpy of vaporization of water.