As the lucy is walking in the constant rate at the starting of her walk to the school.
Thus, the distance is increasing with the time at the constant rate.
This type of velocity is represented in the distance-time graph as a straight line pointing towards the decrease in the remaining distance.
Then the lucy stops for few minutes, which means there is no change in distance with time.
Thus, this motion is represented by a straight line parallel to the time axes.
Then the lucy again start walking towards the school with the slower rate than before.
Thus, the distance traveled in this case with time is smaller than before.
As with the increase of the velocity of lucy, the distance to school decreases.
Thus, fourth graph is the correct answer.