Question

The ordered pairs below represent a relation between x and y.

(-3,0), (-2,4), (-1,8), (0,12), (1,16), (2,20)
could this set of ordered pairs have been generated by a linear function?

Answer 1

Yes, the set of ordered pairs can be generated by a linear function as the differences in the y-values are proportional to the differences in the x-values.

Step-by-step explanation:

Linear functions can be represented by equations in the form y = mx + b, where m and b are constants. In order to determine if the given set of ordered pairs can be generated by a linear function, we can check if the differences in the y-values are proportional to the differences in the x-values.

Let's calculate the differences for each pair of consecutive points:
(-3, 0) to (-2, 4): Difference in x-values: 1, Difference in y-values: 4
(-2, 4) to (-1, 8): Difference in x-values: 1, Difference in y-values: 4
(-1, 8) to (0, 12): Difference in x-values: 1, Difference in y-values: 4
(0, 12) to (1, 16): Difference in x-values: 1, Difference in y-values: 4
(1, 16) to (2, 20): Difference in x-values: 1, Difference in y-values: 4

As we can see, the differences in the y-values are constant for each pair of consecutive points, which indicates a linear relationship. Therefore, this set of ordered pairs can indeed be generated by a linear function.