To determine whether the relationship between time and the amount of popcorn popped is directly proportional, we need to consider the definition of direct proportionality. In a directly proportional relationship, if we plot the values on a graph, we would get a straight line that passes through the origin (0, 0), and the ratio of the output to the input should remain constant.
Let's evaluate the points given in your problem:
- The points (0, 0), (50, 12), and (110, 18) are mentioned.
- The point (0, 0) indicates that at 0 minutes, no popcorn is popped, which is consistent with a directly proportional relationship since it starts at the origin.
- The next point (50, 12) suggests that after 50 minutes, 12 ounces of popcorn has been popped.
- The point (110, 18) indicates that after 110 minutes, 18 ounces of popcorn has been popped.
Now let's check the ratios:
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From (0, 0) to (50, 12):
- Time: 50 minutes, Popcorn: 12 ounces → The ratio is 12 ounces / 50 minutes = 0.24 ounces per minute.
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From (50, 12) to (110, 18):
- Time increase: 110 - 50 = 60 minutes, Popcorn increase: 18 - 12 = 6 ounces → The ratio is 6 ounces / 60 minutes = 0.1 ounces per minute.
Since the ratios (0.24 and 0.1) are not equal, this indicates that the relationship is not constant and therefore not directly proportional.
Additionally, since the relationship does not form a straight line (the change in the quantity of popcorn per time interval varies), it confirms that this relationship is not directly proportional.
Based on this analysis, the correct answer is: No, the graph does not make a straight line.
2 answers