To determine the equation that describes the relationship between time (x) in minutes and the amount of water (y) in gallons, we need to analyze the provided options by considering how the graph might look.
Typically, if we assume that the graph is linear, we can observe two key points on the graph (if available) to derive the slope and y-intercept. Since I can't see the graph directly, let's evaluate the equations based on common scenarios for filling a bathtub.
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Option A: \( y = \frac{x}{4} \)
- This suggests that for every minute that passes, the amount of water increases by \( \frac{1}{4} \) gallons.
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Option B: \( y = 4x \)
- This indicates that for every minute, 4 gallons of water are added to the bathtub.
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Option C: \( y = 15x \)
- Here, for every minute that passes, 15 gallons are added.
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Option D: \( y = \frac{x}{15} \)
- This indicates an increase of \( \frac{1}{15} \) gallons per minute.
To find the correct equation, check the scale of the y-axis (amount of water) in relation to the x-axis (time in minutes). If, for example, the graph indicates that the bathtub fills at a rate of 4 gallons per minute, then option B would be the best fitting equation.
To provide a definitive answer, I would need to see the specific graph you've referenced. However, you can choose the equation based on the rate indicated by the slope of the line on the graph, where the likely candidate will be the one that matches the rate of change in gallons per minute accurately.