Question

The given tables shows the number of active customers for a given time. Match the tables with their function.

• A. Linear, slope = 80
• B. Linear, slope = 0
• C. Non linear function

Answer 1

In this question, we will take time to be "x".
And, number of active customers to be "y".

If the slope of a function is constant, then it is a linear function, else it is a non-linear function.

Let consider Channel A:


Consider the two points (2,250) and (4,410)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{410-250}{4-2}=80$

Now, consider the points (4,410) and (6,570)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{570-410}{6-4}=80$

Since the slope between any two consecutive points are same, the function represented by Channel A is linear.

Slope of function representing Channel A = 80

Let consider Channel B:



Consider the points (2,250) and (4,250).

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{250-250}{4-2}=0$

Since the slope between any two consecutive points is zero, the function represented by channel B is linear.

Slope of function representing Channel B = 0


Let consider Channel C:


Consider the points (2,250) and (4,360)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{360-250}{4-2}=55$

Now, consider the points (6,490) and (4,360)

$\text{Slope}=\frac{\text{Change in y}}{\text{Change in x}}=\frac{490-360}{6-4}=65$

Since the slope between any two consecutive points are not constant throughout, the function represented by Channel C is not linear.