Sara graphs a line passing through points that represent a proportional relationship. Which set of points could be on the line that Sara graphs?
A) (2, 4), (0, 2), (3, 9)
B) (6, 8), (0, 0), (18, 24)
C) (3, 6), (4, 8), (9, 4)
D) (1, 1), (2, 1), (3, 3)
sets where the slope between points is constant form a proportion
To determine which set of points could be on the line that Sara graphs, we need to look for a proportional relationship between the x-values and the y-values.
First, let's check option A) (2, 4), (0, 2), (3, 9):
To find the proportionality, we need to calculate the ratio of the y-values to the x-values:
- For (2, 4): 4/2 = 2
- For (0, 2): 2/0 = Undefined (division by zero)
- For (3, 9): 9/3 = 3
Since the ratio between the y-values and the x-values is not consistent, option A is not a proportional relationship.
Next, let's check option B) (6, 8), (0, 0), (18, 24):
- For (6, 8): 8/6 = 4/3
- For (0, 0): 0/0 = Undefined
- For (18, 24): 24/18 = 4/3
Although the ratio between the y-values and the x-values is consistent (4/3), option B does not represent a proportional relationship because the y-intercept (0, 0) is not present in a proportional relationship.
Moving on to option C) (3, 6), (4, 8), (9, 4):
- For (3, 6): 6/3 = 2
- For (4, 8): 8/4 = 2
- For (9, 4): 4/9 = 4/9
Since the ratio between the y-values and the x-values is not consistent, option C is not a proportional relationship.
Lastly, let's check option D) (1, 1), (2, 1), (3, 3):
- For (1, 1): 1/1 = 1
- For (2, 1): 1/2 = 1/2
- For (3, 3): 3/3 = 1
The ratio between the y-values and the x-values in option D is consistent. It always equals 1. Hence, option D represents a proportional relationship.
Therefore, the set of points that could be on the line that Sara graphs is option D) (1, 1), (2, 1), (3, 3).