Question

A line passing through which of the following pairs of coordinates represents a proportional relationship?
A.
(2, 4) and (5, 6)
B.
(3, 6) and (4, 8)
C.
(1, 3) and (3, 6)
D.
(2, 5) and (4, 6)

Answer 1

A proportional relationship between two coordinates is one where the ratio of the y-values to the x-values is constant for all points. In other words, for a line to represent a proportional relationship, the ratios \( \frac{y}{x} \) for the given points must be equal.

Let's evaluate each option:

A. For the points (2, 4) and (5, 6):
- \( \frac{4}{2} = 2 \)
- \( \frac{6}{5} = 1.2 \)

The ratios are not equal.

B. For the points (3, 6) and (4, 8):
- \( \frac{6}{3} = 2 \)
- \( \frac{8}{4} = 2 \)

The ratios are equal, so this pair represents a proportional relationship.

C. For the points (1, 3) and (3, 6):
- \( \frac{3}{1} = 3 \)
- \( \frac{6}{3} = 2 \)

The ratios are not equal.

D. For the points (2, 5) and (4, 6):
- \( \frac{5}{2} = 2.5 \)
- \( \frac{6}{4} = 1.5 \)

The ratios are not equal.

Thus, the only option that represents a proportional relationship is:

**B. (3, 6) and (4, 8)**