To determine which sketch accurately represents Nina's situation with the rain barrel, we need to analyze the information provided:
- Nina starts with 75 liters of water in the rain barrel.
- Every week, she uses 5 liters of water to water her plants until the barrel is empty.
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Finding the Total Time Until the Barrel is Empty:
- Given that Nina uses 5 liters each week, we can calculate the number of weeks it takes for the barrel to empty: \[ \text{Number of weeks} = \frac{\text{Total water}}{\text{Water used per week}} = \frac{75 \text{ L}}{5 \text{ L/week}} = 15 \text{ weeks} \]
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Creating the endpoints for the graph:
- At week 0, Nina has 75 liters in the rain barrel:
- First endpoint: (0, 75)
- At week 15, the barrel will be empty (0 liters):
- Second endpoint: (15, 0)
- At week 0, Nina has 75 liters in the rain barrel:
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Understanding the Graph:
- The x-axis represents time in weeks, and the y-axis represents the amount of water remaining in liters.
- The correct linear relationship shows a downward slope starting from (0, 75) and ending at (15, 0).
Reviewing the options provided:
- A graph in the first quadrant containing a line segment. The x-axis is labeled Weeks and the y-axis is labeled Liters remaining. The endpoints of the line segment are (0, 15) and (75, 0) - Does not match (incorrect).
- A graph where the endpoints are (0, 5) and (15, 0) - Does not match (incorrect).
- A graph where the endpoints are (0, 75) and (15, 0) - Matches our analysis (correct!).
- A graph where the endpoints are (0, 75) and (5, 0) - Does not match (incorrect).
Conclusion: The correct answer is the graph with endpoints (0, 75) and (15, 0).
1 answer