To analyze the data and graph provided, let's assign each person to a specific line (A, B, C, D) based on the actions they are performing, the distances they are traveling, and the time taken.
A) Explanation of Data Matching Each Line
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Dad - Line A:
- Action: Drives home from the grocery store.
- Distance: 1 mile
- Time: 10 minutes
- Since Dad travels the longest distance of 1 mile in 10 minutes, this represents the slowest speed on the graph, likely line A.
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Aiden - Line B:
- Action: Rides his bike to a friend's house.
- Distance: 0.75 miles
- Time: 10 minutes
- Aiden's speed is greater than Dad's, covering 0.75 miles in the same 10 minutes. This matches to line B, as it would represent a moderate speed.
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Mom - Line C:
- Action: Waits at the doctor's office.
- Distance: 0 miles
- Time: 10 minutes
- Mom's action does not involve any movement, corresponding to line C, which likely represents a stationary position.
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Alexis - Line D:
- Action: Walks to her mailbox down the long driveway.
- Distance: 0.25 miles
- Time: 10 minutes
- Alexis covers the shortest distance of 0.25 miles in the same 10 minutes, thus representing the slowest movement on line D.
B) Description, Comparison, and Contrast of Rates of Speed and Change in Position
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Dad (Line A):
- Speed: 1 mile in 10 minutes translates to a speed of 6 miles per hour.
- Position Change: Dad makes the largest shift in position by covering 1 mile, demonstrating a significant movement from one location to another.
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Aiden (Line B):
- Speed: 0.75 miles in 10 minutes equals a speed of 4.5 miles per hour.
- Position Change: Aiden covers a moderate distance, making him more mobile than Mom and Alexis but less than Dad.
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Mom (Line C):
- Speed: 0 miles implies no movement or speed.
- Position Change: There is no change in her position as she stays stationary, highlighting her passive state compared to the others.
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Alexis (Line D):
- Speed: 0.25 miles in 10 minutes gives a speed of 1.5 miles per hour – the slowest among the group.
- Position Change: Alexis has the smallest change in position, indicating a short walk, thus positioning her as the least active.
Summary of Comparison
- Fastest: Dad is the fastest with a consistent speed, moving the farthest.
- Moderate Speed: Aiden is moderately active but slower than Dad.
- Stationary: Mom remains inactive, experiencing no speed or distance.
- Slowest Walking: Alexis exhibits the least movement, reflecting a leisurely pace.
In conclusion, based on the data, we can claim that Dad corresponds to line A, Aiden to line B, Mom to line C, and Alexis to line D in their respective actions and movement characteristics.