Question

A line passing through which of the following pairs of coordinates represents a proportional relationship?
A.
(1.25, 2.25) and (2.5, 5)
B.
(1.3, 3.3) and (2.3, 4.3)
C.
(1.25, 2.5) and (3.75, 7.5)
D.
(2.5, 5) and (3, 5.5)

Answer 1

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)**.