Ryuk follow Light around and learns more about his plans for becoming a god of a new perfect society.  He also notices a man following him and tells Light.  Light wishes that he knew the man's name so he could take care of him.  Ryuk tells him about a deal that would allow him to do just that.  For just half his remaining life span, he can have Shinigami eyes which would allow him to see everyone's name and the time that they have left to live.