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
[tex]m=\dfrac{d-b}{c-a}.[/tex]
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
[tex] m=\dfrac{5-5}{-4-(-5)}\\\\\\\Rightarrow m=\dfrac{0}{1}\\\\\Rightarrow m=0.[/tex]
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
[tex] m=\dfrac{-4-(-5)}{2-1}\\\\\\\Rightarrow m=\dfrac{1}{1}\\\\\Rightarrow m=1\neq 0.[/tex]
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
[tex] m=\dfrac{4-5}{-4-(-5)}\\\\\\\Rightarrow m=\dfrac{-1}{1}\\\\\Rightarrow m=-1\neq 0.[/tex]
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
[tex] m=\dfrac{-5-(-4))}{5-5}\\\\\\\Rightarrow m=\dfrac{-1}{0}\neq 0.[/tex]
Option (D) is incorrect.
Thus, (A) is the correct option.
