clix - Lesson 2: Exploring Telephone Tariffs

Activity 4: Choosing a Cost-effective Plan Using Graph

To make this task simpler we will plot the graph for each plan category wise; using the graph, we can easily choose the cost-effective plan for Tarun and Prachi.

Lets plot the graph for phone call category of Plan 1.

Plan 1

Category	Charges
Voice Call	₹ 0.50/ minute
Messages	₹ 1/ message
Data	₹ 15/ 100 MB

To plot the graph, we need to understand the relation between voice calls and charges per minute.

In Plan 1, the charges for phone calls are ₹ 0.50/ min; that is, for every minute of a call, the caller will pay ₹ 0.50. We can make a table to see how to calculate the charges for a certain number of minutes.

Time	Calculation	Charges
1 min	1 X 0.50	₹ 0.50
10 min	10 X 0.50	₹ 5
50 min	50 X 0.50	₹ 25
P min	P X 0.50	₹ 0.5P

If we say for x mins the charges are y then we can write the relation as, y = 0.5x,

where x denotes the time in minutes and y denotes the total charges in Rupees. Now, on the x axis we take Time in minutes and on the y axis we take charges in Rupees.

Points for plotting the graph of the equation y = 0.5x are

x (Time in minutes)	y(Charges in ₹ )
10	10 X 0.50 = 5
20	20 X 0.50 = 10
30	30 X 0.50 = 15
40	40 X 0.50 = 20

Graph for the equation y = 0.5x is shown below. It is drawn using Geogebra.

To get help for drawing graphs using Geogebra, refer to help pages.

Here is the tariff plan used by Tarun and Prachi.

Old Plan

Category	Charges
Voice Call	₹ 1/ minute
Messages	₹ 2/ message
Data (Internet)	₹ 250/ 100 MB

To plot the graph, we need to understand the relation of voice calls and charges per minute.

In the old plan, it is given that charges for phone call are ₹ 1/ min, that is for every minute of a call. The caller will pay ₹ 1.

We can make a table for the old plan to see how much charges will be paid.

(Same process need to be repeated as done for Plan 1)

For the old plan, we can say y = x,

where x denotes the time in minutes and y denotes the charges in Rupees.

The comparison graph for Plan 1 and old plan used by Tarun and Prachi for voice call category is shown below.

The green line represents the graph for Plan 1, and the black line represents the graph for the old plan used by Tarun and Prachi.

By looking at the this graph, we can say that the graph line for the old plan used by Tarun and Prachi is slightly higher than Plan 1.

Also, the charges paid for voice calls as per the old plan used by Tarun and Prachi are more than that paid as per Plan 1. (How?)

We can, therefore, conclude that if the graph line for a plan is higher than the graph line of another plan, then, the plan with the higher graph line is costlier than the one with a lower graph line.

If we want to analyse the usage for a particular category of a plan across all the users, then we can do it using slider.

To know more about this refer adding slider in the help page.