Question

The tables given below represents two functions:


is the true statement regarding the behaviour of the above functions.

• A. Function 2 is linear
• B. Function 1 is linear
• C. None of given option

Answer 1

The correct option is B Function 1 is linear

A function is said to be linear if it has a constant slope.

Consider function 1:

x	y
2	12
0	4
4	20

Consider any two coordinates, (2,12) and (0,4).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{4-12}{0-2}$

$\Rightarrow \text{Slope = 4}$

Consider any other two coordinates, say (0,4) and (4,20).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{20-4}{4-0}$

$\Rightarrow \text{Slope = 4}$

Hence the function has constant slope. Therefore it is a linear function.

Consider function 2:

x	y
2	12
1	4
3	16

Consider any two coordinates, say (2,12) and (1,4).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{4-12}{1-2}$

$\Rightarrow \text{Slope = 8}$

Consider any other two coordinates, say (1,4) and (3,16).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{16-4}{3-1}$

$\Rightarrow \text{Slope = 6}$

Hence the function does not has constant slope. Therefore it is not a linear function.