Graph the line that passes through the coordinates below and determine which statement is true.
(1, 2), (3, 4), (5, 6) (7, 8)
A.
The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
B.
The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
C.
The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
D.
The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
In order to determine if the line represents a proportional relationship, we need to check if the ratio of the y-coordinates to the x-coordinates is consistent for all points.
Given the coordinates (1, 2), (3, 4), (5, 6), (7, 8), we can calculate the ratios:
For (1, 2): 2/1 = 2
For (3, 4): 4/3 ≈ 1.33
For (5, 6): 6/5 = 1.2
For (7, 8): 8/7 ≈ 1.14
As we can see, the ratios are not consistent, so the line does not represent a proportional relationship.
Therefore, the correct statement is:
D. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.