To determine whether the relationship between time and the amount of popcorn popped is directly proportional, we look for the characteristics of direct proportionality. In a directly proportional relationship:
- The graph must pass through the origin (0,0).
- The relationship should be linear, meaning a straight line when graphed.
- There should be a consistent ratio between the two variables (e.g., for every X amount of time, there is a fixed amount of popcorn).
Based on the options provided:
- "No, the graph does not go through the origin." indicates that it may not be directly proportional.
- "Yes, the input is time and the output is the amount of popcorn popped." is true but does not confirm direct proportionality.
- "No, the graph does not make a straight line." indicates it is not linear, which disqualifies direct proportionality.
- "Yes, for every 10 minutes there were 4 ounces of popcorn popped." could suggest a relationship, but without knowing if this is consistent (e.g., does it stay the same over time?), it's not enough.
From the responses, it seems the relationship is not directly proportional because either the graph does not go through the origin or does not form a straight line. Therefore, the best conclusion would be:
No, the graph does not go through the origin.
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