Final answer:
Without specific numerical slope values, only statement A about the rate of change representing hourly babysitting charges can be definitively confirmed as true, based on the understanding of graph slopes.
Step-by-step explanation:
When analyzing the statements about the given graph regarding babysitting services and their rates of change, we must use the information related to slopes of the lines represented on the graph. The rate of change on a graph corresponds to the slope of the lines, which in the context of babysitting services, would indicate how much a person charges per hour.
If line A is steeper than line B and increasing, it indicates that person A has a higher rate of change and thus charges more per hour than person B. Conversely, if line B is steeper, then person B charges more per hour. A negative slope implies that as the number of hours increases, the total cost decreases, which does not align with the concept of hourly payment for services. Therefore, without specific numerical values provided for the slopes, we cannot definitively answer whether statements B, C, D, E, or F are true. However, we can affirm that statement A is true as it correctly describes the relationship between the rate of change and the hourly charges for babysitting services.