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To determine the values of \( A \) and \( B \) for the scatter graph, we need to analyze the range of the data and select an appropriate scale.

The values in the table are as follows:

- **Time (seconds)**: 71, 135, 14, 116, 58
- **Height (meters)**: 29, 37, 6, 31, 18

### Steps to Determine \( A \) and \( B \)

1. **Identify the Range for Each Axis**:
   - **For Time** (horizontal axis): The minimum value is 14, and the maximum is 135. So, the range is from 14 to 135.
   - **For Height** (vertical axis): The minimum value is 6, and the maximum is 37. So, the range is from 6 to 37.

2. **Choose the Scale**:
   - For **Time**, a reasonable scale could have intervals that accommodate the range from 0 to around 140.
   - For **Height**, a scale that covers from 0 to 40 would be sufficient.

3. **Define \( A \) and \( B \)**:
   - \( A \) is likely the maximum value for **Time** on the graph, which would be slightly above 135 (likely rounded to 140 for ease).
   - \( B \) is the maximum for **Height**, so we can set it to 40.

### Final Answer:
- **\( A = 140 \)**
- **\( B = 40 \)**

Would you like a further breakdown of the steps or an explanation of how to plot these points?

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### Additional Questions for Practice:
1. How would you choose the scale if the values had a larger range?
2. What if the height values were negative? How would that affect \( B \)?
3. Can you describe the process of plotting a scatter graph step-by-step?
4. How would you find the mean of the height values?
5. If another point was added with time 200, what would the new \( A \) value be?

### Tip:
Always choose scales that allow for easy division of the graph's range, which helps in accurate plotting and interpretation.

Time will be plotted on the horizontal axis below. If the best scale is used to plot the data, what are the values of A and B?

Learn how to determine the values of A and B for plotting time and height data on a scatter graph. This problem involves data interpretation and graph scaling, suitable for students in Grades 6-8.

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