Question

The dots represents the number of games played by three different schools in different years.

After joining all same coloured dots. Which of the following have linear function.

• A. School A
• B. School B
• C. School C
• D. None

Answer 1

The correct option is A School A

If the rate of change of a function is constant, then we can say that it is linear function.

$\text{The rate of change}=\frac{\text{Change in y}}{\text{Change in x}}$

Let's find out rate of change of school A

Year (x)	2015	2016	2017
No. of matches played (y)	20	30	40

$\text{Slope}=\frac{30-20}{2016-2015}=\frac{40-30}{2017-2016}=10$

Therefore, it is a linear function.

Let's find out rate of change of school B

Year (x)	2015	2016	2017
No. of matches played (y)	10	20	26

$\text{Slope}=\frac{20-10}{2016-2015}\ne \frac{26-20}{2017-2016}$

Therefore, it is not a linear function.

School C is not function because it has two outputs for a single input.