To determine whether the relationship is proportional, we need to check if the rate of portraits painted per hour is constant.
Let's calculate the rates for each case:
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For 2 portraits in 8 hours: \[ \text{Rate} = \frac{2 \text{ portraits}}{8 \text{ hours}} = \frac{1}{4} \text{ portraits per hour} \]
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For 3 portraits in 12 hours: \[ \text{Rate} = \frac{3 \text{ portraits}}{12 \text{ hours}} = \frac{1}{4} \text{ portraits per hour} \]
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For 5 portraits in 20 hours: \[ \text{Rate} = \frac{5 \text{ portraits}}{20 \text{ hours}} = \frac{1}{4} \text{ portraits per hour} \]
In all cases, the rate is the same: \( \frac{1}{4} \) portraits per hour.
Since the rate of painting is consistent, this indicates a proportional relationship. In a proportional relationship, if the graph of the data is plotted, it should form a straight line through the origin (0,0).
Given these points:
- The relationship is proportional.
- The graph should form a straight line through the origin.
Thus, the correct statement is:
C. The given situation represents a proportional relationship because the graph of the given data forms a straight line through the origin.