Class 8 RD Sharma Solutions - Chapter 27 Introduction to Graphs - Exercise 27.2

Exercise 27.2 from Chapter 27 "Introduction to Graphs" in RD Sharma's Class 8 mathematics textbook focuses on understanding and applying the concepts of graphs. This exercise typically covers topics such as plotting points on a coordinate plane, identifying coordinates of given points, and understanding the relationship between x and y coordinates.

Question 1. The following table shows the number of patients discharged from a hospital with HIV diagnosis in different years:

Represent the information by a graph.

Solution:

From the question as we know that, 

The number of patients - is a dependent variable.

Year - is an independent variable.

Take years on x-axis

and Number of patients on y - axis

Choose the following scale:

X - axis: 2 cm = 1 year

Y - axis: 1 cm = 10 patients

Consider that on the x-axis, origin (O) represents 2001 and on the y-axis, origin (O) represents 120, 

i.e. O (2001, 120).

Now, Plot 

(2002, 150), 

(2003, 170), 

(2004, 195), 

(2005, 225), 

(2006, 230). 

Join these points in the following graph as shown below.

👁 Image

Question 2. The following table shows the amount of rice grown by a farmer in different years:

Plot a graph to illustrate this information.

Solution:

From the question as we know that, 

Year - is an independent variable 

Quantity of rice grown is a dependent variable. 

So, take

Year on X - axis

Quantity of rice grown on Y - axis 

Choose following scale:

X - axis: 2 cm = 1 year

Y - axis: 1 cm = 20 quintals

Consider that the origin O represents the coordinates (1999, 160).

i.e. O (1999,160)

Now, Plot 

(2000, 200), 

(2001, 180), 

(2002, 240), 

(2003, 260), 

(2004, 250),

(2005, 200),

(2006, 270).

Join these points on the following graph as shown below:

👁 Image

Question 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:

Plot the graph of this information.

Solution:

From the question as we know that,  

The number of persons - is an independent variable

Time taken - is a dependent variable.

So, take 

The number of persons on the X - axis 

Time taken on the Y - axis.

Choose following scale:

X - axis: 2 cm = 2 persons

Y - axis: 2 cm = 2 days

Now, plot 

(2, 12), 

(4, 6), 

(6, 4), 

(8, 3).

Join these points on the following graph as shown below:

👁 Image

Question 4. The following table gives the information regarding length of a side of a square and its area

Draw a graph to illustrate this information.

Solution:

From the question as we know that, 

Length of a side - is an independent variable

Area of the square - is a dependent variable.

So, take 

Length of a side on the X - axis 

Area of the square on the Y - axis.

Choose following scale:

X - axis: 2 cm = 1 cm

Y - axis: 1 cm = 2 cm²

Now, plot 

(1, 1), 

(2, 4), 

(3, 9), 

(4, 16), 

(5, 25).

Join these points in the following graph as shown below:

👁 Image

Question 5. The following table shows the sales of a commodity during the years 2000 to 2006.

Draw a graph of this information.

Solution:

From the question as we know that, 

Year - is an independent variable 

Sales - is a dependent variable. 

So, take 

Year on the X - axis 

Sales on the Y - axis.

Choose following scale:

X - axis: 2 cm = 1 year

Y - axis: 2 cm = 1 lakh rupees

Consider that on x-axis, origin (O) represents 1991.

Hence, the coordinates of O are (1991, 0).

Now, plot 

(2000, 1.5), 

(2001, 1.8), 

(2002, 2.4), 

(2003, 3.2), 

(2004, 5.4), 

(2005, 7.8) 

(2006, 8.6).

Join these points on the following graph as shown below;

👁 Image

Question 6. Draw the temperature-time graph in each of the following cases:

(i) 

(ii)

Solution:

(i) From the question as we know that, 

Time - is an independent variable 

Temperature - is a dependent variable. 

So, take 

Time on the X - axis 

Temperature on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 hour

Y - axis: 1 cm = 1°F

Consider that on the x-axis, the coordinate of origin is 6:00.

On y-axis, the coordinate of origin is 94°F.

Hence, the coordinates of 0 are (6:00, 94).

Now, plot 

(7:00, 100), 

(9:00, 101), 

(11:00, 104)

(21:00, 98)

Join these points on the following graph as shown below:

👁 Image

(ii) From the question we know that, 

Time - is an independent variable 

Temperature - is a dependent variable. 

So, take 

Time on the X - axis 

Temperature on the Y - axis.

Choose following scale:

X - axis: 2 cm = 2 hours

Y - axis: 1 cm = 1°F

Consider that on the x-axis, the coordinate of origin is 6:00.

On y-axis, the coordinate of origin is 94°F.

Thus, the coordinates of 0 are (6:00, 94).

Now, plot 

(8:00, 100), 

(10:00, 101), 

(12:00, 104)….. 

(20:00, 100).

Join these points on the graph as shown below:

👁 Image

Question 7. Draw the velocity-time graph from the following data:

Solution:

From the question as we know that, 

Time - is an independent variable. 

Speed - is a dependent variable. 

So, take 

Time on the X - axis 

Speed on the Y - axis.

Choose following scale:

X - axis: 2 big division = 1 hour

Y - axis: 1 big division = 10 km/hr

Consider that on the x-axis, the coordinate of origin (O) is 7:00.

Thus, the coordinates of O are (7:00, 0).

Now, plot 

(7:00, 30), 

(8:00, 45), 

(9:00, 60), 

(10:00, 50), 

(11:00, 70), 

(12:00, 50), 

(13:00, 40), 

(14:00, 45).

Join these points on the graph as shown below:

👁 Image

Question 8.The runs scored by a cricket team in first 15 overs are given below:

Draw the graph representing the above data in two different ways as a graph and as a bar chart.

Solution:

From the question as we know that, 

Over - is an independent variable. 

Run is a dependent variable. 

So, take 

Overs on the X - axis 

Runs on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 over

Y - axis: 1 cm = 2 runs

Now, plot 

(I, 2), 

(II, 1), 

(III, 4)… 

(XV, 12).

Join these points on graph as shown below:

👁 Image

The bar graph is:

👁 Image

Question 9. The runs scored by two teams A and B in first 10 overs are given below:

Draw a graph depicting the data, making the graphs on the same axes in each case in two different ways as a graph and as a bar chart.

Solution:

From the question as we know that, 

Over - is an independent variable. 

Run - is a dependent variable. 

So, take 

Overs on X - axis 

Runs on the Y - axis.

Choose following scale:

X - axis: 1 cm = 1 over

Y - axis: 1 cm = 1 run

Now, plot 

(I, 2), 

(II, 1), 

(III, 8)… 

(X, 2) for team A 

and 

(I, 5), 

(II, 6), 

(III, 8) ….. 

(X, 10) for team B.

Join these points on graph as shown below:

👁 Image

The bar graph is:

👁 Image

Summary

Exercise 27.2 in RD Sharma's Class 8 textbook provides students with practice in graphing points on a coordinate plane, understanding the relationship between x and y coordinates, and applying basic concepts of analytical geometry. Through various questions, students learn to plot points, identify coordinates, and analyze the properties of points in different quadrants of the coordinate system.