Final answer:
The distance from home is constant when the graph of position versus time is a horizontal line.
Step-by-step explanation:
The distance from home is constant when the graph of position versus time is a horizontal line. This means that the object is not changing its position over time, so the distance remains the same. In the given scenario, when the parent was driving at a constant velocity, the distance from home would be constant during the time it took to make the drive.