Question

Table $1$ and Table $2$ represent functions.

Choose the table(s) representing the linear function(s).

Answer 1

We know that, in a linear function, the rate of change is constant for any two points on the line.

Table 1

Given,Let’s consider a set of two points $(8,8)\text{and}(10,10)$.

Slope $=\frac{\text{Change in y}}{\text{Change in x}}=\frac{(10-8)}{(10-8)}=\frac{2}{2}=1$

Consider another set of two points $(10,10)\text{and}(13,13)$.
Slope $=\frac{\text{Change in y}}{\text{Change in x}}=\frac{(13-10)}{(13-10)}=\frac{3}{3}=1$

Consider another set of two points $(13,13)\text{and}(16,16)$.
Slope $=\frac{\text{Change in y}}{\text{Change in x}}=\frac{(16-13)}{(16-13)}=\frac{3}{3}=1$

Since the slope is constant, the function represented by the given table is linear.

Table 2

Given:
Let’s consider a set of two points $(17,20)\text{and}(18,14)$.

Slope $=\frac{\text{CChange in y}}{\text{CChange in x}}=\frac{(14-20)}{(18-17)}=\frac{-6}{1}=-6$

Consider another set of two points $(18,14)\text{and}(19,7)$.
Slope $=\frac{\text{Change in y}}{\text{Change in x}}=\frac{(7-14)}{(19-18)}=\frac{-7}{1}=-7$

Consider another set of two points $(19,7)\text{and}(20,2)$.
Slope $=\frac{\text{Change in y}}{\text{Change in x}}=\frac{(2-7)}{(20-19)}=\frac{-5}{1}=-5$

Since the slope is constant, the function represented by the given table is linear.

Option A is correct.