1. A graph generation apparatus comprising: a processor to execute a program; and a memory to store the program, past graph point group data, and new graph point group data, wherein the past graph point group data represents, in chronological order, a plurality of graph points included in a past line graph, the new graph point group data represents, in chronological order, a plurality of graph points included in a new line graph, and the program which, when executed by the processor, results in performance of steps comprising, selecting, as overlapping-portion data, graph point group data which represents a plurality of graph points included in an overlapping-portion graph, the overlapping-portion graph being a line graph of a time period of the past line graph where the new line graph overlaps, from the past graph point group data, and generating graph image data that represents, as the overlapping-portion graph, a line graph in which a display style of the overlapping-portion data gradually changes along a time axis.