Question

The data in which table represents a linear function that has a slope of zero?

A. X Y
-5 5
-4 5
-3 5
-2 5
-1 5

B. X Y
1 -5
2 -4
3 -3
4 -2
5 -1

C. X Y
-5 5
-4 4
-3 3
-2 2
-1 1

D. X Y
5 -5
5 -4
5 -3
5 -2
5 -1

Answer 1

The correct answer is A

Answer 2

Answer: The correct option is (A).

Step-by-step explanation: We are given to select the data in which the table represents a linear function that has a slope of zero.

We know that

the slope of a data having two pairs of values (a, b) and (c, d) is given by

`m=(d-b)/(c-a).`

Data (A) : Here we note that the two pairs of values are (-5, 5) and (-4, 5).

So, the slope of the data will be

`m=(5-5)/(-4-(-5))\\\\\\\Rightarrow m=(0)/(1)\\\\\Rightarrow m=0.`

Option (A) is CORRECT.

Data (B) : Here we note that the two pairs of values are (1, -5) and (2, -4).

So, the slope of the data will be

`m=(-4-(-5))/(2-1)\\\\\\\Rightarrow m=(1)/(1)\\\\\Rightarrow m=1\\eq 0.`

Option (B) is incorrect.

Data (C) : Here we note that the two pairs of values are (-5, 5) and (-4, 4).

So, the slope of the data will be

`m=(4-5)/(-4-(-5))\\\\\\\Rightarrow m=(-1)/(1)\\\\\Rightarrow m=-1\\eq 0.`

Option (C) is incorrect.

Data (D) : Here we note that the two pairs of values are (5, -5) and (5, -4).

So, the slope of the data will be

`m=(-5-(-4)))/(5-5)\\\\\\\Rightarrow m=(-1)/(0)\\eq 0.`

Option (D) is incorrect.

Thus, (A) is the correct option.