To determine the correct equation that describes the relationship between time (x, in minutes) and the amount of water (y, in gallons) in the bathtub, we need to analyze the graph you mentioned. Since I can't visualize the graph, I'll guide you on how to approach it.
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Identify the Axes: See which axis represents time (x) and which represents the amount of water (y).
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Look for Key Points: Find two clear points on the graph that indicate the amount of water at specific times. For example, if at 0 minutes (x = 0), y = 0 gallons, and at 4 minutes (x = 4), y = 15 gallons (hypothetical values), this will inform the relationship.
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Calculate the Rate of Change: If the amount of water increases evenly over time, calculate how much water is added per minute (slope). For example, if y increases by 15 gallons over 4 minutes, the rate would be \( \frac{15}{4} \) gallons per minute.
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Match with Options: Once you identify the slope (rise/run), see which of the provided equations corresponds to that relationship.
Without the actual graph, I recommend using the above steps. However, based on these options:
- A. \( y = \frac{x}{4} \): This suggests a very slow fill rate.
- B. \( y = 4x \): This suggests a fast fill rate.
- C. \( y = 15x \): This is very steep and implies 15 gallons per minute.
- D. \( y = \frac{x}{15} \): Very slow fill again.
Given these options, if the bathtub fills steadily and uniformly, look for an equation that directly relates x (time) to y (water) with a suitable coefficient based on what you observed from the graph.
If you find typical values that make sense (like 4 gallons in 1 minute), then B. \( y = 4x \) may be reasonable if, for example, it corresponds to a linear increase.
Conclusion: It depends on the specific data points you've derived from the graph. If you have the values at key points, simply insert them into the equations to see which one holds true. If you can describe the graph’s key points, I could help deduce the correct answer further.
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