Question
Every week, Nina used 5 L of water from her rain barrel to water her plants. She did this until her rain barrel was empty. When Nina first started watering, her rain barrel contained 75 L of water.
Which sketch represents this situation?
Responses
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 begin ordered pair 0 comma 15 end ordered pair and begin ordered pair 75 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 15 end ordered pair and begin ordered pair 75 comma 0 end ordered pair.
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 begin ordered pair 0 comma 5 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 5 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 5 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 5 comma 0 end ordered pair.
Which sketch represents this situation?
Responses
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 begin ordered pair 0 comma 15 end ordered pair and begin ordered pair 75 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 15 end ordered pair and begin ordered pair 75 comma 0 end ordered pair.
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 begin ordered pair 0 comma 5 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 5 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 15 comma 0 end ordered pair.
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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 5 comma 0 end ordered pair.
Image with alt text: 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 begin ordered pair 0 comma 75 end ordered pair and begin ordered pair 5 comma 0 end ordered pair.
Answers
GPT-4o mini
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.
1. **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:
\[
\text{Number of weeks} = \frac{\text{Total water}}{\text{Water used per week}} = \frac{75 \text{ L}}{5 \text{ L/week}} = 15 \text{ weeks}
\]
2. **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)
3. **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).**
- 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.
1. **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:
\[
\text{Number of weeks} = \frac{\text{Total water}}{\text{Water used per week}} = \frac{75 \text{ L}}{5 \text{ L/week}} = 15 \text{ weeks}
\]
2. **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)
3. **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).**