Activity 4: Choosing the Cost-Effective Plan Using Graph
To simplify this task, 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.
Let us 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 charge for voice calls is ₹ 0.50/ min i.e. 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
x min
x X 0.50
₹ 0.5x
If we consider the talk time as x mins and the total charges as y ₹ then, we can write the relation as, y = 0.5x.
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
Now, we need to plot at least two of the points (10, 5), (20, 10), (30, 15), (40, 20) in order to the get our line. The graph for the equation y = 0.5x as plotted using GeoGebra is shown in the below GIF:
A snapshot of the line plotted in GeoGebra environment is shown below:
To get help for drawing graphs using Geogebra, refer to helppages.
Here are the tariff plans 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 again consider the relation of voice calls and charges per minute.
In the old plan, it is given that charge for voice calls is ₹ 1/ min i.e. for every minute of a call the caller will have to pay ₹ 1. We can make a table for the old plan to see what charges will be paid (the same process needs 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 this graph, we can say that the graph line for the old plan used by Tarun and Prachi is slightly higher than Plan 1. We can say that the black line has a larger angle of rotation from the x-axis than what the green line has. 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 sliders. To know more about using sliders in GeoGebra, please refer to the "adding a slider" section in the help page.
LINEAR EQUATIONS
Activity 4: Choosing the Cost-Effective Plan Using Graph
To simplify this task, 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.
Let us 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 charge for voice calls is ₹ 0.50/ min i.e. 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
x min
x X 0.50
₹ 0.5x
If we consider the talk time as x mins and the total charges as y ₹ then, we can write the relation as, y = 0.5x.
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
Now, we need to plot at least two of the points (10, 5), (20, 10), (30, 15), (40, 20) in order to the get our line. The graph for the equation y = 0.5x as plotted using GeoGebra is shown in the below GIF:
Replay Animation
A snapshot of the line plotted in GeoGebra environment is shown below:
To get help for drawing graphs using Geogebra, refer to help pages.
Here are the tariff plans 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 again consider the relation of voice calls and charges per minute.
In the old plan, it is given that charge for voice calls is ₹ 1/ min i.e. for every minute of a call the caller will have to pay ₹ 1. We can make a table for the old plan to see what charges will be paid (the same process needs 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 this graph, we can say that the graph line for the old plan used by Tarun and Prachi is slightly higher than Plan 1. We can say that the black line has a larger angle of rotation from the x-axis than what the green line has. 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 sliders. To know more about using sliders in GeoGebra, please refer to the "adding a slider" section in the help page.