Final answer:
The x-intercept in a distance versus time graph represents the time it takes to reach the destination, which is the school in this scenario. After calculating the rate of travel, it's determined that the x-intercept is (27, 0), signifying that it takes 27 minutes to reach the school.
Step-by-step explanation:
The x-intercept in a graph of distance versus time in a physics context represents the point where the distance becomes zero, implying that the object has arrived at its destination. In the scenario described, the student seeks to find the x-intercept for the distance from school as a function of time. The table in the question illustrates a linear relationship between the distance from the school and time, suggesting a constant rate of change or velocity.
By examining the given values, one can note that the distance from the school decreases by 4 meters every 3 minutes. Extrapolating this data, we can determine that the x-intercept should be when the distance is zero. If you start at 36 meters away and approach the school at a constant rate, the point at which the distance reaches zero would indicate the time it takes to reach the school.
None of the options (36, 0) or (27, 0) provided in the question scientifically represent the x-intercept. To find the correct x-intercept, we need to calculate the rate at which the student approaches the school and then determine how long it takes to cover a distance of 36 meters at that rate. Since the distance decreases by 4 meters every 3 minutes, we divide 36 meters by 4 meters per 3 minutes to find the time it takes to reach the school, which is 27 minutes. Therefore, the correct interpretation of the x-intercept would be (27, 0); this denotes the time it takes to reach the school.