"Dynamic" Line Chart

You need to define two dynamic ranges, one for the dates and one for the data
Presuming Your dates start at F1 and your data starts at G1, go to

Insert > Name > Define

OFFSET($F$1,MATCH($A$1,$F$1:$F$19,0)-1,0,MATCH($B$1,$F$1:$F$19)-MATCH($A$1,$F$1:$F$19,0)+1,1)

assign a name such as graphdates

then

=OFFSET(graphdates,0,1)

assigned a name such as graphdata


Then create the graph, and use these two names ranges as the dataset.