Based on the description provided, let’s analyze each of the statements:
1. **The student will earn four points on the quiz if she plays eight hours of video games.**
This statement would depend on the data points on the graph, which we cannot see, but if you find that the corresponding quiz score for eight hours is indeed four points, then this statement would be correct. However, without seeing the graph, we cannot confirm its validity.
2. **The point (10, 5) shows that the student earned 10 points on the quiz after playing video games for five hours.**
This statement is incorrect based on the standard conventions of graphing. The x-coordinate denotes hours spent playing video games, and the y-coordinate denotes the points scored. Therefore, (10, 5) means the student scored 5 points after playing for 10 hours, not the other way around.
3. **There is a positive relationship between the number of points scored on the quiz and the number of hours spent playing video games.**
If indeed the graph shows an upward trend, where more hours spent playing correlates with higher quiz scores, then this statement would be correct. Again, without the graph, we can't verify this.
4. **The student’s quiz score goes down by one point for every two hours she spent on video games.**
This statement describes a negative correlation. If the graph indeed shows that as hours increase, scores decrease, then this statement would be correct. However, without confirmation from the graph, this cannot be determined.
Given these evaluations, the most scientifically reasonable answer, assuming there's no visible negative relationship in the graph, might be the third statement regarding a positive relationship, as it is the most common expectation in such studies unless stated otherwise. However, please refer to the graph to make a final conclusion.