On a temperature versus time graph, how does the temperature at the beginning of a change of state compare with the temperature at the end of the change?

The temperature is the same. During a phase change, a sample is gaining heat with out a change in temperature since all of the energy is being put into the breaking of the intermolecular forces which makes it so that the average kinetic energy of the particles in the substance does not change (the energy is not used to speed up the particles). I hope this helps. Let me know if anything is unclear. (I used a phase change that is gaining heat shuch as boiling and if you reverse my explanation it explains a phase change that is loosing heat such as freezing).