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Which of the following statements about the set of ordered pairs (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11) is accurate? Could this set of ordered pairs have been generated by a linear function?

Option 1: No, because the y-values decrease and then increase.
Option 2: 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.
Option 3: Yes, because the distance between consecutive x-values is constant.
Option 4: No, because the distance between consecutive y-values is different than the distance between consecutive x-values.

1 Answer

4 votes

Final answer:

The set of ordered pairs is generated by a linear function, with each pair showing a consistent increase in the y-value relative to the x-value, which indicates a constant slope. Therefore, Option 2 is correct.

Step-by-step explanation:

The set of ordered pairs in question can certainly be generated by a linear function. This function would have a constant slope, meaning that for every increase in the x-value, there is a proportional and consistent increase in the y-value. To determine if a set of ordered pairs represents a linear function, one can calculate the slope between each pair.

Looking at the pairs given, (-3,1), (-2,3), (-1,5), (0,7), (1,9), (2,11), we see that the x-values increase by 1 each time, and the y-values increase by 2 each time. This consistency confirms that the slope is constant. For instance:

(-2,3) to (-1,5) involves an increase of 1 in x and an increase of 2 in y, so the slope is 2/1 = 2. If we check another pair, (0,7) to (1,9), the change in x is +1 and the change in y is +2, which again gives us a slope of 2. Since the slope between consecutive pairs of points remains the same, we can conclude that these points lie on a line with a slope of 2.

Therefore, the correct statement is: 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. Hence, Option 2 is the accurate description of the given set of ordered pairs.

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