Question

A line represents a proportional relationship. Which set of points could be on the line? Responses A (−4, −2), (2, 1), (6, 3), (14,7)(−4, −2), (2, 1), (6, 3), (14,7) B (6, 8), (4, 0), (18, 24), (20, 26)(6, 8), (4, 0), (18, 24), (20, 26) C (3, 6), (4, 8), (9, 4), (11, 2)(3, 6), (4, 8), (9, 4), (11, 2) D (1, 1), (2, 1), (3, 3), (4, 2)

Answer 1

[AI-generated answer — Bot GPT 3.5]

A proportional relationship means that for every increase in the x-coordinate, there is a corresponding increase or decrease in the y-coordinate.

Looking at the points in set A, we can see that for each x-coordinate increase of 6 (from -4 to 2 to 6 to 14), the y-coordinate increases by 3 (from -2 to 1 to 3 to 7). Therefore, set A could represent a proportional relationship.

Looking at the points in set B, we can see that for each x-coordinate increase of 2 (from 4 to 6 to 18 to 20), the y-coordinate increases by 8 (from 0 to 8 to 24 to 26). Therefore, set B could represent a proportional relationship.

Looking at the points in set C, we can see that the relationship between the x-coordinate and y-coordinate is not consistent. As the x-coordinate increases from 3 to 4, the y-coordinate increases from 6 to 8. However, as the x-coordinate increases from 9 to 11, the y-coordinate decreases from 4 to 2. Therefore, set C does not represent a proportional relationship.

Looking at the points in set D, we can see that the relationship between the x-coordinate and y-coordinate is not consistent. As the x-coordinate increases from 1 to 2, the y-coordinate stays the same at 1. However, as the x-coordinate increases from 3 to 4, the y-coordinate increases from 3 to 2. Therefore, set D does not represent a proportional relationship.

In conclusion, the sets of points that could be on the line representing a proportional relationship are A and B.