A proportional relationship between two coordinates means that the ratio of the \( y \)-value to the \( x \)-value is constant.
Let's check each pair:
A. \((1.25, 2.25)\) and \((2.5, 5)\)
For (1.25, 2.25): \[ \frac{y}{x} = \frac{2.25}{1.25} = 1.8 \]
For (2.5, 5): \[ \frac{y}{x} = \frac{5}{2.5} = 2 \]
Since \( 1.8 \neq 2 \), this does not represent a proportional relationship.
B. \((1.25, 2.5)\) and \((3.75, 7.5)\)
For (1.25, 2.5): \[ \frac{y}{x} = \frac{2.5}{1.25} = 2 \]
For (3.75, 7.5): \[ \frac{y}{x} = \frac{7.5}{3.75} = 2 \]
Since both ratios are equal to \( 2 \), this represents a proportional relationship.
C. \((1.3, 3.3)\) and \((2.3, 4.3)\)
For (1.3, 3.3): \[ \frac{y}{x} = \frac{3.3}{1.3} \approx 2.54 \]
For (2.3, 4.3): \[ \frac{y}{x} = \frac{4.3}{2.3} \approx 1.87 \]
Since \( 2.54 \neq 1.87 \), this does not represent a proportional relationship.
D. \((2.5, 5)\) and \((3, 5.5)\)
For (2.5, 5): \[ \frac{y}{x} = \frac{5}{2.5} = 2 \]
For (3, 5.5): \[ \frac{y}{x} = \frac{5.5}{3} \approx 1.83 \]
Since \( 2 \neq 1.83 \), this does not represent a proportional relationship.
The only pair that represents a proportional relationship is B. (1.25, 2.5) and (3.75, 7.5).
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