You're not stuck when you have gaps in your data- here's how to work around with your chart.
The exercise and result are in the Chart Gaps file.
Here is some simple sales data.

Note we have a gap, so here is what would happen with a line chart.

Fortunately, Excel offers some options. Go to the Tools menu and select Options. Then select the Chart tab.

This gives a number of options for the empty cells like we had:
Not plotted- leave a gap as we have
Zero- not good in this case for a line chart
Interpolated- which would fill in the trend. We will choose that.

Now we have a more presentable graph. The line is continued but without showing a data point.
One other point. This is chart specific. If you do another chart with the same data, that chart will have a gap, unless go back in again and change it as we did here.
Take advantage to the chart options for blank cells to best fit your situation- blank, zero or interpolated.