Which two ordered pairs represent a proportional relationship?
A.
(3, 3) and (6, 6)
B.
(3, 3) and (6, 9)
C.
(5, 4) and (6, 6)
D.
(4, 3) and (6, 6)
The answer is C. (5, 4) and (6, 6) because the ratio of the y-values is always the same: 4/5 = 6/6.
To determine if two ordered pairs represent a proportional relationship, we can check if the ratio between the x-coordinates is equal to the ratio between the y-coordinates.
Let's evaluate each option:
A. (3, 3) and (6, 6)
The ratio of the x-coordinates is 3/6 = 1/2
The ratio of the y-coordinates is 3/6 = 1/2
Since the ratios are equal, this option represents a proportional relationship.
B. (3, 3) and (6, 9)
The ratio of the x-coordinates is 3/6 = 1/2
The ratio of the y-coordinates is 3/9 = 1/3
The ratios are not equal, so this option does not represent a proportional relationship.
C. (5, 4) and (6, 6)
The ratio of the x-coordinates is 5/6
The ratio of the y-coordinates is 4/6 = 2/3
The ratios are not equal, so this option does not represent a proportional relationship.
D. (4, 3) and (6, 6)
The ratio of the x-coordinates is 4/6 = 2/3
The ratio of the y-coordinates is 3/6 = 1/2
The ratios are not equal, so this option does not represent a proportional relationship.
Therefore, the answer is option A: (3, 3) and (6, 6) represent a proportional relationship.