To determine which equation describes the relationship between \( x \) (the time in minutes) and \( y \) (the amount of water in gallons), we need to consider what a realistic relationship might look like.
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Option A: \( y = \frac{x}{4} \) suggests that as time increases, the amount of water decreases, which doesn't make sense in a typical scenario.
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Option B: \( y = 4x \) suggests that for every minute, 4 gallons of water is produced or consumed, which is a plausible positive correlation.
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Option C: \( y = 15x \) suggests that for every minute, 15 gallons of water is produced or consumed, which is also plausible but indicates a faster rate than Option B.
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Option D: \( y = \frac{x}{15} \) suggests a decrease in water amount as time increases, which also doesn't make sense.
Based on the typical assumptions for such relationships, either Option B \( y = 4x \) or Option C \( y = 15x \) could be reasonable depending on the context (e.g., a flow rate or consumption rate). If we assume a constant rate with reasonable values, Option B \( y = 4x \) is generally a good baseline for a context where water is accumulating over time.
Thus, the equation that most likely describes the relationship is:
B. \( y = 4x \)
1 answer