A proportional relationship can be identified by checking if the ratios of the y-values to the x-values are constant between the pairs of coordinates.
Let's evaluate each pair:
A. (1.25, 2.25) and (2.5, 5)
- Ratio for (1.25, 2.25): \( \frac{2.25}{1.25} = \frac{2.25 \times 100}{1.25 \times 100} = \frac{225}{125} = \frac{9}{5} = 1.8 \)
- Ratio for (2.5, 5): \( \frac{5}{2.5} = \frac{5 \times 100}{2.5 \times 100} = \frac{500}{250} = 2 \)
Different ratios, not proportional.
B. (1.3, 3.3) and (2.3, 4.3)
- Ratio for (1.3, 3.3): \( \frac{3.3}{1.3} \approx 2.53846 \)
- Ratio for (2.3, 4.3): \( \frac{4.3}{2.3} \approx 1.86957 \)
Different ratios, not proportional.
C. (1.25, 2.5) and (3.75, 7.5)
- Ratio for (1.25, 2.5): \( \frac{2.5}{1.25} = 2 \)
- Ratio for (3.75, 7.5): \( \frac{7.5}{3.75} = 2 \)
Same ratios, proportional.
D. (2.5, 5) and (3, 5.5)
- Ratio for (2.5, 5): \( \frac{5}{2.5} = 2 \)
- Ratio for (3, 5.5): \( \frac{5.5}{3} \approx 1.83333 \)
Different ratios, not proportional.
The only pair that represents a proportional relationship is C. (1.25, 2.5) and (3.75, 7.5).