The ordered pairs below represent a relation between x and y. (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11). Could this set of ordered pairs have been generated by a linear function?. A) Yes, because the distance between consecutive x-values is constant. B) No, because the distance between consecutive y-values is different than the distance between consecutive x-values. C) Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it. D) No, because the y-values decrease and then increas

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Mathematics

Areli

4 September, 23:04

The ordered pairs below represent a relation between x and y. (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11). Could this set of ordered pairs have been generated by a linear function?. A) Yes, because the distance between consecutive x-values is constant. B) No, because the distance between consecutive y-values is different than the distance between consecutive x-values. C) Yes, because the relative difference between y-values and x-values is the same no matter which pairs of (x, y) values you use to calculate it. D) No, because the y-values decrease and then increas

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Rhett Stein · Answer 1

First, look at the values of the abscissas: - 3, - 2, - 1, 0, and 1. The values form an arithmetic sequence with common difference of 1. On the other hand the values of the ordinates: 1, 3, 5, 7, and 9 also form an arithmetic sequence with common difference of 2. Since the coordinates form arithmetic sequences, the answer to the question above is letter C.