The ordered pairs below represent a relation between x and ,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. no, because the distance between consecutive y-values is different than the distance between consecutive x-valuesb. yes, because the distance between consecutive x-values is constantc. 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 itd. no, because the y-values decrease and then increase

The correct answer is C.

Step-by-step explanation:

Notice that the difference between consecutive values of x is always 1, and the difference between consecutive values of y is always 2. This means that

where and stands for two consecutive values of x, and the same goes to y.

Now, notice that this is the definition of the slope of the equation of a line. Then, a line can be characterized by this condition, and that is why C is the correct answer.

Anyway, you can check that this set of point is generated by a linear function in other way. Suppose that it can be done, and the linear function has the form

.

From the pair (0,7) we deduce that , then . Now, substituting the pair (-3,1) we get and as consequence . Thus, if the points are generated by a linear function, its expression would be .

Now, substitute the different values of x and check that the same values of y are obtained.

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step-by-step explanation:

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