To analyze the statements based on the graph with the slope from (0, 0) to (110, 22), we can determine the following:
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Statement A: "The unit rate for the amount of protein grams per tablespoon of peanut butter is 25 grams of protein per tablespoon of peanut butter."
- Evaluation: The slope can be calculated as the change in protein over the change in tablespoons. From the points (0, 0) to (110, 22), we have 22 grams of protein over 110 tablespoons. The unit rate (slope) is \( \frac{22}{110} = \frac{1}{5} \) or 0.2 grams per tablespoon, not 25 grams.
- Conclusion: FALSE
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Statement B: "The line passes through the origin, therefore it models a proportional relationship."
- Evaluation: Since the line passes through the origin (0, 0), it does indeed suggest a proportional relationship. If it were a proportional relationship, the quantities would have a constant ratio.
- Conclusion: TRUE
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Statement C: "Point (6,30) means there are 30 grams of protein in 6 tablespoons of peanut butter."
- Evaluation: The point (6, 30) indicates that for 6 tablespoons of peanut butter, there are 30 grams of protein. However, based on the given slope (0.2 grams per tablespoon), in reality, 6 tablespoons contain \( 6 \times 0.2 = 1.2 \) grams of protein.
- Conclusion: FALSE
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Statement D: "The graph does not represent a proportional relationship."
- Evaluation: Since the graph passes through the origin and is a straight line, it does represent a proportional relationship.
- Conclusion: FALSE
Based on this analysis, the only true statement is B.
2 answers