Question

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)}

Answer 1

Explanation:

Answer 2

Question:

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

`\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}`

`\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}`

`\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}`

`\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}`

Answer:

`\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}`

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.

`m = (y_2 - y_1)/(x_2-x_1)`

Considering A:

`\mathbf{A}= \,\,\left\{(2, 9),\,\,(4, 5),\,\,(6, 1),\,\,(7, -1)\right\}`

Consider the following pairs

`(x_1,y_1) = (2,9)` and
`(x_2,y_2) = (4,5)`

`m = (5 - 9)/(4 -2) = (-4)/(2) = -2`

Consider the another pairs

`(x_1,y_1) = (2,9)` and
`(x_2,y_2) = (6,1)`

`m = (1 - 9)/(6 -2) = (-8)/(4) = -2`

Consider the another pairs

`(x_1,y_1) = (2,9)` and
`(x_2,y_2) = (7,-1)`

`m = (-1 - 9)/(7 -2) = (-10)/(5) = -2`

The slope is uniform all through.

i.e.

`m = -2`

Hence, this can be a linear function

Considering B:

`\mathbf{B}= \,\,\left\{(-1, -8),\,\,(0, -3),\,\,(1, 3),\,\,(2, 8)\right\}`

Consider the following pairs

`(x_1,y_1) = (-1,-8)` and
`(x_2,y_2) = (0,-3)`

`m = (-3 - (-8))/(0 - (-1)) = (-3 +8)/(0 +1) = (5)/(1) = 5`

Consider the another pairs

`(x_1,y_1) = (-1,-8)` and
`(x_2,y_2) = (1,3)`

`m = (3 - (-8))/(1 - (-1)) = (3 +8)/(1 +1) = (11)/(2) = 5.5`

The calculated slopes are not equal.

i.e.

`m = 5` and
`m = 5.5`

Hence, this can't be a linear function

Considering C:

`\mathbf{C}= \,\,\left\{(-9, 5),\,\,(-3, 3),\,\,(3, 0),\,\,(9, -2)\right\}`

Consider the following pairs

`(x_1,y_1) = (-9,5)` and
`(x_2,y_2) = (-3,3)`

`m=(3-5)/(-3-(-9)) = (3-5)/(-3+9) = (-2)/(6) = -(1)/(3)`

Consider the another pairs

`(x_1,y_1) = (-9,5)` and
`(x_2,y_2) = (3,0)`

`m=(0-5)/(3-(-9)) = (0-5)/(3+9) = (-5)/(12) = -(5)/(12)`

The calculated slopes are not equal.

i.e.

`m = -(5)/(12)` and
`m = -(1)/(3)`

Hence, this can't be a linear function

Considering D:

`\mathbf{D}= \,\,\left\{(1, -8),\,\,(2, -6),\,\,(3, -3),\,\,(4, 0)\right\}`

Consider the following pairs

`(x_1,y_1) = (1,-8)` and
`(x_2,y_2) = (2,-6)`

`m = (-6 - (-8))/(2 - 1) = (6 + 8)/(1) = (14)/(1) = 14`

Consider the another pairs

`(x_1,y_1) = (1,-8)` and
`(x_2,y_2) = (3,-3)`

`m = (3 - (-8))/(-3 - 1) = (3 + 8)/(-4) = (11)/(-4) = -(11)/(4)`

The calculated slopes are not equal.

i.e.

`m = -(11)/(4)` and
`m = 14`

Hence, this can't be a linear function

From the calculations above:

Only (A) can be a linear function