Introduction to Graphs - Exercise 27.2 | Mathematics (Maths) Class 8 PDF Download

 Page 1


 
 
 
 
 
 
 
                                                      
 
1. The following table shows the number of patients discharged from a hospital with 
HIV diagnosis in different years: 
Years 2002 2003 2004 2005 2006 
Number of 
Patients 
150 170 195 225 230 
Represent the information by a graph. 
Solution: 
Here we know, year is an independent variable and the number of patients is a dependent 
variable. So let us take years on the x-axis and the number of patients on the y-axis. 
Let us choose the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 10 patients 
 
Let us assume that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) 
represents 120, i.e. O (2001, 120). 
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These 
points are joined to get the graph representing the given information as shown in the 
figure below. 
 
Page 2


 
 
 
 
 
 
 
                                                      
 
1. The following table shows the number of patients discharged from a hospital with 
HIV diagnosis in different years: 
Years 2002 2003 2004 2005 2006 
Number of 
Patients 
150 170 195 225 230 
Represent the information by a graph. 
Solution: 
Here we know, year is an independent variable and the number of patients is a dependent 
variable. So let us take years on the x-axis and the number of patients on the y-axis. 
Let us choose the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 10 patients 
 
Let us assume that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) 
represents 120, i.e. O (2001, 120). 
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These 
points are joined to get the graph representing the given information as shown in the 
figure below. 
 
 
 
 
 
 
 
 
 
2. The following table shows the amount of rice grown by a farmer in different 
years: 
Years 2000 2001 2002 2003 2004 2005 2006 
Rice 
grown (in 
quintals) 
200 180 240 260 250 200 270 
Plot a graph to illustrate this information. 
Solution: 
We know that, the year is an independent variable and quantity of rice grown is a 
dependent variable. So let us take years on the x-axis and quantity of rice grown on the y-
axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 20 quintals 
Let us assume that the origin O represents the coordinates (1999, 160). 
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 
200),(2006, 270). 
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
Page 3


 
 
 
 
 
 
 
                                                      
 
1. The following table shows the number of patients discharged from a hospital with 
HIV diagnosis in different years: 
Years 2002 2003 2004 2005 2006 
Number of 
Patients 
150 170 195 225 230 
Represent the information by a graph. 
Solution: 
Here we know, year is an independent variable and the number of patients is a dependent 
variable. So let us take years on the x-axis and the number of patients on the y-axis. 
Let us choose the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 10 patients 
 
Let us assume that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) 
represents 120, i.e. O (2001, 120). 
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These 
points are joined to get the graph representing the given information as shown in the 
figure below. 
 
 
 
 
 
 
 
 
 
2. The following table shows the amount of rice grown by a farmer in different 
years: 
Years 2000 2001 2002 2003 2004 2005 2006 
Rice 
grown (in 
quintals) 
200 180 240 260 250 200 270 
Plot a graph to illustrate this information. 
Solution: 
We know that, the year is an independent variable and quantity of rice grown is a 
dependent variable. So let us take years on the x-axis and quantity of rice grown on the y-
axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 20 quintals 
Let us assume that the origin O represents the coordinates (1999, 160). 
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 
200),(2006, 270). 
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
3. The following table gives the information regarding the number of persons 
employed to a piece of work and time taken to complete the work: 
Number of 
persons 
2 4 6 8 
Time taken (in 
days) 
12 6 4 3 
Plot the graph of this information. 
Solution: 
We know, the number of persons is an independent variable and time taken is a 
dependent variable.  
So, we take the number of persons on the x-axis and time taken on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 2 persons 
On y-axis: 2 cm = 2 days 
Now, let us plot (2, 12), (4, 6), (6, 4), (8, 3).  
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
Page 4


 
 
 
 
 
 
 
                                                      
 
1. The following table shows the number of patients discharged from a hospital with 
HIV diagnosis in different years: 
Years 2002 2003 2004 2005 2006 
Number of 
Patients 
150 170 195 225 230 
Represent the information by a graph. 
Solution: 
Here we know, year is an independent variable and the number of patients is a dependent 
variable. So let us take years on the x-axis and the number of patients on the y-axis. 
Let us choose the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 10 patients 
 
Let us assume that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) 
represents 120, i.e. O (2001, 120). 
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These 
points are joined to get the graph representing the given information as shown in the 
figure below. 
 
 
 
 
 
 
 
 
 
2. The following table shows the amount of rice grown by a farmer in different 
years: 
Years 2000 2001 2002 2003 2004 2005 2006 
Rice 
grown (in 
quintals) 
200 180 240 260 250 200 270 
Plot a graph to illustrate this information. 
Solution: 
We know that, the year is an independent variable and quantity of rice grown is a 
dependent variable. So let us take years on the x-axis and quantity of rice grown on the y-
axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 20 quintals 
Let us assume that the origin O represents the coordinates (1999, 160). 
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 
200),(2006, 270). 
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
3. The following table gives the information regarding the number of persons 
employed to a piece of work and time taken to complete the work: 
Number of 
persons 
2 4 6 8 
Time taken (in 
days) 
12 6 4 3 
Plot the graph of this information. 
Solution: 
We know, the number of persons is an independent variable and time taken is a 
dependent variable.  
So, we take the number of persons on the x-axis and time taken on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 2 persons 
On y-axis: 2 cm = 2 days 
Now, let us plot (2, 12), (4, 6), (6, 4), (8, 3).  
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
4. The following table gives the information regarding length of a side of a square 
and its area 
Length of a 
side (in cm) 
1 2 3 4 5 
Area of 
square (in 
cm
2
) 
1 4 9 16 25 
Draw a graph to illustrate this information. 
Solution: 
We know, length of a side is an independent variable and area of the square is a 
dependent variable.  
So, let us take the length of a side on the x-axis and area of the square on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 cm 
On y-axis: 1 cm = 2 cm
2
 
Now, let us plot (1, 1), (2, 4), (3, 9), (4, 16), (5, 25).  
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
Page 5


 
 
 
 
 
 
 
                                                      
 
1. The following table shows the number of patients discharged from a hospital with 
HIV diagnosis in different years: 
Years 2002 2003 2004 2005 2006 
Number of 
Patients 
150 170 195 225 230 
Represent the information by a graph. 
Solution: 
Here we know, year is an independent variable and the number of patients is a dependent 
variable. So let us take years on the x-axis and the number of patients on the y-axis. 
Let us choose the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 10 patients 
 
Let us assume that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) 
represents 120, i.e. O (2001, 120). 
Now, let us plot (2002, 150), (2003, 170), (2004, 195), (2005, 225), (2006, 230). These 
points are joined to get the graph representing the given information as shown in the 
figure below. 
 
 
 
 
 
 
 
 
 
2. The following table shows the amount of rice grown by a farmer in different 
years: 
Years 2000 2001 2002 2003 2004 2005 2006 
Rice 
grown (in 
quintals) 
200 180 240 260 250 200 270 
Plot a graph to illustrate this information. 
Solution: 
We know that, the year is an independent variable and quantity of rice grown is a 
dependent variable. So let us take years on the x-axis and quantity of rice grown on the y-
axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 1 cm = 20 quintals 
Let us assume that the origin O represents the coordinates (1999, 160). 
Now, let us plot (2000, 200), (2001, 180), (2002, 240), (2003, 260), (2004, 250),(2005, 
200),(2006, 270). 
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
3. The following table gives the information regarding the number of persons 
employed to a piece of work and time taken to complete the work: 
Number of 
persons 
2 4 6 8 
Time taken (in 
days) 
12 6 4 3 
Plot the graph of this information. 
Solution: 
We know, the number of persons is an independent variable and time taken is a 
dependent variable.  
So, we take the number of persons on the x-axis and time taken on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 2 persons 
On y-axis: 2 cm = 2 days 
Now, let us plot (2, 12), (4, 6), (6, 4), (8, 3).  
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
4. The following table gives the information regarding length of a side of a square 
and its area 
Length of a 
side (in cm) 
1 2 3 4 5 
Area of 
square (in 
cm
2
) 
1 4 9 16 25 
Draw a graph to illustrate this information. 
Solution: 
We know, length of a side is an independent variable and area of the square is a 
dependent variable.  
So, let us take the length of a side on the x-axis and area of the square on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 cm 
On y-axis: 1 cm = 2 cm
2
 
Now, let us plot (1, 1), (2, 4), (3, 9), (4, 16), (5, 25).  
These points are joined to get the graph representing the given information as shown in 
the figure below. 
 
 
 
 
 
 
 
 
 
5. The following table shows the sales of a commodity during the years 2000 to 2006. 
Years 2000 2001 2002 2003 2004 2005 2006 
Sales (in 
lakhs of 
Rs) 
1.5 1.8 2.4 3.2 5.4 7.8 8.6 
Draw a graph of this information. 
Solution: 
We know, year is an independent variable and sales is a dependent variable. So, we take 
year on the x-axis and sales on the y-axis. 
By choosing the following scale: 
On x-axis: 2 cm = 1 year 
On y-axis: 2 cm = 1 lakh rupees 
Assume that on x-axis, origin (O) represents 1991. 
So, the coordinates of O are (1991, 0). 
Now, let us plot (2000, 1.5), (2001, 1.8), (2002, 2.4), (2003, 3.2), (2004, 5.4), (2005, 7.8) 
and (2006, 8.6).  
These points are joined to get the graph representing the given information as shown in 
the figure below.