To analyze Alonso's walking, let's calculate his walking rate and complete the table of distance versus time.
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Rate of walking:
Alonso walked 1 mile in 0.5 hours. \[ \text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{1 \text{ mile}}{0.5 \text{ hours}} = 2 \text{ miles per hour} \] -
Completing the table:
If Alonso walks at a constant pace of 2 miles per hour, we can calculate the distance for various times. For example:- At 0.5 hours, distance = 1 mile
- At 1 hour, distance = 2 miles
- At 1.5 hours, distance = 3 miles
- At 2 hours, distance = 4 miles
This would create a table like:
| Time (hours) | Distance (miles) | |--------------|------------------| | 0 | 0 | | 0.5 | 1 | | 1 | 2 | | 1.5 | 3 | | 2 | 4 |
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Graphing the relationship:
When graphed, the points will form a straight line passing through (0,0) and increasing linearly, demonstrating a consistent rate of distance covered over time. -
Evaluating the statements:
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The line passes through the origin.
True: Since at 0 hours, the distance is 0 miles (0,0). -
The relationship is proportional.
True: The relationship is linear and the distance increases at a constant rate (2 miles per hour), thus showing a constant ratio. -
Alonso walks 0.5 miles per hour.
False: He walks 2 miles per hour, not 0.5. -
There is no constant of proportionality.
False: The constant of proportionality is 2 (miles/hour).
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Thus, the true statements are that the line passes through the origin and the relationship is proportional.
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