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?

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.