Which set of ordered pairs (x, y)(x, y) could represent a linear function? \mathbf{A}= A= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\} {(2,9),(4,5),(6,1),(7,−1)} \mathbf{B}= B= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\} {(−1,−8),(0,−3),(1,3),(2,8)} \mathbf{C}= C= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\} {(−9,5),(−3,3),(3,0),(9,−2)} \mathbf{D}= D= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\} {(1,−8),(2,−6),(3,−3),(4,0)}

Question:

Which set of ordered pairs (x,y) could represent a linear function?

Step-by-step explanation:

Given

Ordered pairs A - D

Required

Which represents a linear function?

To do this, we simply calculate the slope (m) of each ordered pairs.

Considering A:

Consider the following pairs

and

Consider the another pairs

and

Consider the another pairs

and

The slope is uniform all through.

i.e.

Hence, this can be a linear function

Considering B:

Consider the following pairs

and

Consider the another pairs

and

The calculated slopes are not equal.

i.e.

and

Hence, this can't be a linear function

Considering C:

Consider the following pairs

and

Consider the another pairs

and

The calculated slopes are not equal.

i.e.

and

Hence, this can't be a linear function

Considering D:

Consider the following pairs

and

Consider the another pairs

and

The calculated slopes are not equal.

i.e.

and

Hence, this can't be a linear function

From the calculations above:

Only (A) can be a linear function

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step-by-step explanation: