Jack tracked the average amount of time he and his friend spent playing video games each day. He plotted the average for each day and added a best-fit line. 



Using the best-fit line, which of the following is TRUE?


A.)
They spent 50 minutes playing video games on Day 6.


B.)
They spent about 41 minutes playing video games on Day 2.


C.)
They likely spent about 40 minutes playing video games before they started tracking (Day 0).


D.)
They will likely spend about 64 minutes playing video games on Day 8.

To determine which statement is true based on the best-fit line, we need to interpret what a best-fit line represents. A best-fit line shows the general trend in the data by estimating values that may not be explicitly provided in the dataset. From this, we can make predictions about the amount of time Jack and his friend spent playing video games on specific days or even on days not directly tracked.

Let's analyze the choices:

1. **Option A: "They spent 50 minutes playing video games on Day 6."**  
   - This implies that the exact amount of time they spent playing on Day 6 was 50 minutes. A best-fit line, however, typically provides an estimated average, not an exact time for each day. The exact figure may vary from the data points. Thus, this statement is unlikely to be true unless the best-fit line specifically passes through 50 minutes on Day 6, which would be unusual for exact data points.

2. **Option B: "They spent about 41 minutes playing video games on Day 2."**  
   - "About" indicates an approximation, which aligns with the idea of a best-fit line offering an estimate. If the best-fit line suggests that around 41 minutes were spent on Day 2, this could be true. 

3. **Option C: "They likely spent about 40 minutes playing video games before they started tracking (Day 0)."**  
   - This statement makes a prediction based on extrapolation, which the best-fit line is often used for. If the best-fit line, when extended backward to Day 0, suggests a value close to 40 minutes, this could be true. Without specific values or a graph, we can't confirm the exact number, but it's plausible based on extrapolation.

4. **Option D: "They will likely spend about 64 minutes playing video games on Day 8."**  
   - Similar to Option C, this prediction is based on extrapolation. If the best-fit line projects an estimated 64 minutes on Day 8, this statement could be true. Again, without the graph, we can't confirm, but this is a reasonable interpretation of how a best-fit line works.

### Conclusion:
The statement that is most likely to be true based on the nature of a best-fit line and the provided context is **Option C: "They likely spent about 40 minutes playing video games before they started tracking (Day 0)."** 

Would you like further details or have any questions? Here are some related questions you might consider:

1. What is a best-fit line, and how is it calculated?
2. How can we use a best-fit line to make predictions about untracked data?
3. How accurate are predictions based on a best-fit line?
4. Can we always trust a best-fit line to reflect the actual trend of the data?
5. What are other methods to analyze trends in a dataset?

**Tip:** Best-fit lines are often created using linear regression, a statistical method for finding the line that best approximates the relationship between variables.

Jack tracked the average amount of time he and his friend spent playing video games each day. He plotted the average for each day and added a best-fit line. Using the best-fit line, which of the following is TRUE? A.) They spent 50 minutes playing video games on Day 6. B.) They spent about 41 minutes playing video games on Day 2. C.) They likely spent about 40 minutes playing video games before they started tracking (Day 0). D.) They will likely spend about 64 minutes playing video games on Day 8.

Learn how to use a best-fit line to analyze Jack's video game time trends and make predictions for untracked days. Explore key concepts such as linear regression, extrapolation, and how to interpret the equation of a line. This problem is suitable for students in Grades 8-10.

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