Question

A line passing through which of the following pairs of coordinates represents a proportional relationship?

A.
(2, 4) and (5, 6)
B.
(1, 3) and (3, 6)
C.
(3, 6) and (4, 8)
D.
(2, 5) and (4, 6)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine if a relationship is proportional, we need to check if the ratio of the y-coordinate to the x-coordinate is constant for each pair of points.

Let's calculate the ratios for each pair of points:

A. (2, 4) and (5, 6)
Ratio for the first pair: 4/2 = 2
Ratio for the second pair: 6/5 = 1.2
Since the ratios are not the same, this pair does not represent a proportional relationship.

B. (1, 3) and (3, 6)
Ratio for the first pair: 3/1 = 3
Ratio for the second pair: 6/3 = 2
Since the ratios are not the same, this pair does not represent a proportional relationship.

C. (3, 6) and (4, 8)
Ratio for the first pair: 6/3 = 2
Ratio for the second pair: 8/4 = 2
Since the ratios are the same, this pair represents a proportional relationship.

D. (2, 5) and (4, 6)
Ratio for the first pair: 5/2 = 2.5
Ratio for the second pair: 6/4 = 1.5
Since the ratios are not the same, this pair does not represent a proportional relationship.

Therefore, the line passing through the coordinates (3, 6) and (4, 8) represents a proportional relationship. The answer is C.