QUESTION IMAGE
Question
making signs
claire and alison are making signs for all the lockers as part of the decorations for the upcoming spirit week. yesterday, alison made 15 signs and claire made 5 signs. today, they need to make more signs. each person’s progress today is shown in the coordinate plane.
- which line represents claire’s progress? which line represents alison’s progress? explain how you know.
- based on the lines, mark the statements as true or false for each person.
| point | what it says | claire | alison |
|---|---|---|---|
| b | at 75 minutes, i have 42 and a half signs completed. | ||
| c | at 0 minutes, i have 15 signs completed. | ||
| d | at 100 minutes, i have 60 signs completed. |
- what do you notice about the point/statement(s) that was true for both claire and alison?
Brief Explanations
- For question 1: Start with the initial number of signs each made yesterday. Claire began today with 5 signs, so her line has a y-intercept of 5. Alison began today with 15 signs, so her line has a y-intercept of 15. Then compare the slopes: Alison's line is steeper, meaning she makes signs faster, which aligns with her higher total by the end of the graph.
- For question 2:
- Point A: Both lines intersect at (40, 25), so this is true for both.
- Point B: This lies on the steeper line (Alison's), not Claire's, so true only for Alison.
- Point C: This is the y-intercept of the flatter line (Claire's, starting with 15 total? No, correction: Wait, Claire made 5 yesterday, so her starting point today is 5? No, wait the y-axis is total completed signs. So Claire's total starts at 5, Alison's at 15. So point C is (0,15) which is Alison's starting total, so true for Alison, false for Claire.
- Point D: This lies on Alison's steeper line, not Claire's, so true only for Alison.
- For question 3: The only statement true for both is the point where their lines cross, meaning at that exact time, they had completed the same total number of signs combined from yesterday and today.
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- The steeper line (with points A, B, D) represents Alison's progress. The flatter line (with points C, A) represents Claire's progress.
- Explanation: Alison started today with 15 signs already made (y-intercept of 15), and Claire started with 5 signs (y-intercept of 5). The steeper line has a higher starting value (15) and shows faster progress, matching Alison's higher initial count and faster rate. The two lines intersect at point A, meaning at 40 minutes, they had both completed 25 total signs.
2.
| point | what it says | Claire | Alison |
|---|---|---|---|
| B | At 75 minutes, I have 42 and a half signs completed. | False | True |
| C | At 0 minutes, I have 15 signs completed. | False | True |
| D | At 100 minutes, I have 60 signs completed. | False | True |
- The only statement true for both Claire and Alison (point A) is the intersection point of their two lines. This means at 40 minutes, Claire and Alison had completed the exact same total number of signs (25) when combining the signs they made yesterday and today.