A line passing through which of the following pairs of coordinates represents a proportional relationship? A. (2, 5) and (4, 6) B. (3, 6) and (4, 8) C. (2, 4) and (5, 6) D. (1, 3) and (3, 6)
In a proportional relationship, the ratio between the y-coordinates and the x-coordinates should be the same for all points on the line.
Let's check each pair of coordinates:
A. (2, 5) and (4, 6)
The ratio of the y-coordinates is 6/5, but the ratio of the x-coordinates is 4/2 = 2.
Since the ratios do not match, these points do not represent a proportional relationship.
B. (3, 6) and (4, 8)
The ratio of the y-coordinates is 8/6 = 4/3.
The ratio of the x-coordinates is 4/3.
Since the ratios match, these points represent a proportional relationship.
C. (2, 4) and (5, 6)
The ratio of the y-coordinates is 6/4 = 3/2.
The ratio of the x-coordinates is 5/2.5 = 2.
Since the ratios do not match, these points do not represent a proportional relationship.
D. (1, 3) and (3, 6)
The ratio of the y-coordinates is 6/3 = 2.
The ratio of the x-coordinates is 3/1 = 3.
Since the ratios do not match, these points do not represent a proportional relationship.
The only pair of coordinates that represent a proportional relationship is option B. (3, 6) and (4, 8).