Based on the description of the line graph, let's analyze the statements:
1. **The student will earn four points on the quiz if she plays eight hours of video games.**
- This would depend on the specific data shown in the graph at 8 hours. If the graph indicates that the score at 8 hours is indeed 4 points, this statement is correct. Otherwise, it's incorrect.
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. The (x,y) format shows that for 5 hours of video games (x), the score (y) is 10 points, 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 the points scored increase with an increase in hours played, then this statement would be correct, indicating a positive correlation.
4. **The student’s quiz score goes down by one point for every two hours she spent on video games.**
- If the graph shows a decreasing trend in points with increasing hours played, this statement could be correct. This would imply a negative slope for the function.
Without seeing the actual line graph, I can't definitively state which answer is correct. However, if the graph indicates that points increase with hours played, then the third statement would be the most likely correct statement. If the graph shows the opposite trend, then perhaps the fourth statement could be accurate.