To graph the scenario where Catherine sells boxes of cookies, follow these steps:
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Understand the Data:
- Starting number of boxes: 135
- Selling rate: 15 boxes per day
- Time period until cookies are sold out: \( \frac{135}{15} = 9 \) days. She will have 0 boxes left after 9 days.
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Create a Table of Values:
- You can create a table that shows how many boxes are left at the end of each day.
| Days (x) | Boxes Left (y) | |----------|-----------------| | 0 | 135 | | 1 | 120 | | 2 | 105 | | 3 | 90 | | 4 | 75 | | 5 | 60 | | 6 | 45 | | 7 | 30 | | 8 | 15 | | 9 | 0 | | 10 | 0 | | 11 | 0 |
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Set Up the Graph:
- X-axis (Time in Days): This axis will represent the days (from 0 to 11).
- Y-axis (Boxes Left to Sell): This axis will represent how many boxes are left (from 0 to 135, or up to 150 for the scale).
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Plot the Points:
- Plot each point from the table on the graph:
- (0, 135)
- (1, 120)
- (2, 105)
- (3, 90)
- (4, 75)
- (5, 60)
- (6, 45)
- (7, 30)
- (8, 15)
- (9, 0)
- (10, 0)
- (11, 0)
- Plot each point from the table on the graph:
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Draw Segments:
- Connect the points with straight lines. The graph will begin at (0, 135) and have a downward slope until (9, 0). After day 9, the line will remain flat along the horizontal line at 0 boxes sold for days 10 and 11.
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Label Your Graph:
- You can label the axes ("Days" for the x-axis and "Boxes Left to Sell" for the y-axis), and also give the graph a title like "Catherine's Cookie Sales."
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Analyze the Graph:
- You will observe that the graph is linear (straight line) until the 9th day, demonstrating a steady decrease in the number of boxes sold at a rate of 15 per day, followed by a flat line indicating no more boxes left after day 9.
Once you have completed these steps, you will have successfully graphed the number of boxes Catherine has left to sell over time!
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