Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states? A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (20, 1) and (40, 2). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (1, 20) and (2, 40). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (0, 5) and (1, 6). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (5, 0) and (6, 1).
Question
Some states pay $0.05 for each can that is recycled. Which graph represents the amount of money earned, y, by recycling x cans in these states? A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (20, 1) and (40, 2). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (1, 20) and (2, 40). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (0, 5) and (1, 6). A graph titled Recycling Money has cans on the x-axis and dollars on the y-axis. A line goes through points (5, 0) and (6, 1).
Solution
The correct graph would be the one that shows a direct relationship between the number of cans recycled (x) and the amount of money earned (y). Since each can is worth $0.05, the slope of the line should be 0.05.
Looking at the options:
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The first graph has points (20, 1) and (40, 2). This means for 20 cans you get 2. This is a correct representation because the ratio of dollars to cans is 1:20 or $0.05 per can.
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The second graph has points (1, 20) and (2, 40). This means for 1 can you get 40. This is not a correct representation because the ratio of dollars to cans is 20:1 or $20 per can.
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The third graph has points (0, 5) and (1, 6). This means for 0 cans you get 6. This is not a correct representation because you shouldn't get money for recycling 0 cans.
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The fourth graph has points (5, 0) and (6, 1). This means for 5 cans you get 1. This is not a correct representation because the ratio of dollars to cans is 1:6 or approximately $0.17 per can.
So, the correct graph is the first one.
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