The administrative fee is paid at the beginning of each year, when months have passed. This is the intercept of the graphs.
We can see above that the intercept of the line which corresponds to Family 1 is greater than the one of Family 2. This means that Family 1 paid a higher administrative fee.
The monthly cost is a payment done every month. In the graph, this is represented by the slope of the lines. Thus, if they have the same slope, the monthly cost will be the same. Let's identify rise and run between two points on the lines.
The rise and run is the same between two points on the lines. This means that their slope will be the same as well. Lines with the same slope are said to be parallel. Therefore, the families pay the same monthly fee.