To determine which object would reach 100 feet in the least amount of time based on the provided lines and coordinates, we need to analyze the slopes of each line. The slope of a line in a distance-time graph represents the speed; a steeper slope means a greater speed.
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Line A passes through the points (0, 0) and (3, 6).
- The slope is calculated as (change in distance)/(change in time) = (6 - 0)/(3 - 0) = 6/3 = 2 feet/second.
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Line B passes through the points (0, 0) and (6, 6).
- The slope is (6 - 0)/(6 - 0) = 6/6 = 1 foot/second.
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Line C passes through the points (0, 0) and (6, 3).
- The slope is (3 - 0)/(6 - 0) = 3/6 = 0.5 feet/second.
Now, we can find the time it would take each object to reach 100 feet using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
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For Line A: \[ \text{Time} = \frac{100 \text{ feet}}{2 \text{ feet/second}} = 50 \text{ seconds} \]
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For Line B: \[ \text{Time} = \frac{100 \text{ feet}}{1 \text{ foot/second}} = 100 \text{ seconds} \]
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For Line C: \[ \text{Time} = \frac{100 \text{ feet}}{0.5 \text{ feet/second}} = 200 \text{ seconds} \]
From this analysis, the object represented by Line A reaches 100 feet in the least amount of time, which is 50 seconds.
Final answer: object A.
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