# NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

**NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs: ** In daily life, you must have seen different types of graphs like in newspapers- business analysis, on television -cricket match comparison of the score of two teams, or score of a player over a period of time or in books, etc. What is a graph? What is the purpose of graphs? What are the types of graphs? In NCERT solutions for class 8 maths chapter 15 introduction to graphs, you will get answers to all these questions. The graph is a visual representation of data. The purpose of the graph is to show collected data or numerical facts in visual form so that anyone can understand it easily, quickly and clearly.

Graphs have the ability to compare and reveal a trend, so it is better to represent data in a graph rather than in a table. In NCERT solutions for class 8 introduction to graphs, you will find different types of graphs like- Bar graph, Histogram, Pie graph ( or pie chart or a circle graph), Line graph, and Linear graph in the 3 exercises. These different type of graphs that you will use depends on your data and need. If data changes continuously with the time you will be using a line graph. You can use histogram(bar graph) to show data in any intervals. There are 3 exercises with 65 questions in NCERT the textbook. All these questions are explained in NCERT solutions for class 8 maths chapter 15 introduction to graphs which will build basic knowledge about the graphs. You can get NCERT solutions from class 6 to 12 to by clicking on the above link. Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

** Topics of NCERT class 8 maths chapter 15- Introduction to Graphs **

- 15.1 Introduction
- 15.1.1 A Bar graph
- 15.1.2 A Pie graph (or a circle-graph)
- 15.1.3 A histogram
- 15.1.4 A line graph
- 15.2 Linear Graphs
- 15.2.1 Location of a point
- 15.2.2 Coordinates
- 15.3 Some Applications

** NCERT solutions for class 8 maths chapter 15 Introduction to Graphs for all the exercises **

** NCERT solutions for class 8 chapter 15 introduction to graphs-Exercise: 15.1 **

** Question:1(a) ** The following graph shows the temperature of a patient in a hospital , recorded every hour .

What was the patient's temperature at 1 p.m

** Answer: **

(a) The patient's temperature at 1 p.m is celsius.

** Question:1(b) ** The following graph shows the temperature of a patient in a hospital recorded every hour.

When was the patients temperature ?

** Answer: **

(b) The patients temperature is at 12 noon.

** Question:1(c) ** The following graph shows the temperature of a patient in a hospital recorded every hour.

** Answer: **

(c) The patients temperature was the same two times during the period given these two times are 1 p.m. and 2 p.m.

** Question:1(d) ** The following graph shows the temperature of a patient in a hospital recorded every hour.

What was the temperature at 1:30 p.m? How did you arrive at your answer?

** Answer: **

(d) The temperature at 1:30 p.m is celsius. The temperature at 1 p.m. to 2 p.m. is same i.e. celsius so it is also same as at 1:30 p.m is celsius.

** Question:1(e) ** The following graph shows the temperature of a patient in a hospital recorded every hour.

During which periods did the patients temperature showed an upward trend ?

** Answer: **

(e) The patients temperature showed an upward trend- 9 am to 10 am., 10 am. to 11 am. and 2pm to 3pm

** Question:2(a) ** The following line graph shows the yearly sales figure for a manufacturing company.

What are the sales in (1) 2002 (2) 2006 ?

** Answer: **

(a) The sales in

(1) 2002 = 4 crore

(2) 2006 = 8 crore

** Question:2(b) ** The following line graph shows the yearly sales figure for a manufacturing company.

What are the sales in (1) 2003 (2) 2005 ?

** Answer: **

(b) The sales in

(1) 2003 = 7 crore

(2) 2005 = 10 crore

** Question:2(c) ** The following line graph shows the yearly sales figure for a manufacturing company.

Compute the difference between sales in 2002 and 2006

** Answer: **

(c) The difference between sales in 2002 and 2006 .

** Question:2(d) ** The following line graph shows the yearly sales figure for a manufacturing company

In which year was there the greatest difference between the sales as compared to its previous year ?

** Answer: **

(d) The greatest difference between the sales as compared to its previous year is between 2004 and 2005.

How high was Plant A after (i) 2 weeks (ii) 3 weeks?

** Answer: **

(a) The Plant A after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 9 cm height.

** Answer: **

(b) The Plant B after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 10cm height.

How much did Plant B grow from the end of the 2nd week to the end of the 3rd week?

** Answer: **

(d)The Plant B grow from the end of the 2nd week to the end of the 3rd week height.

During which week did Plant A grow most?

** Answer: **

(e)The week in which Plant A grow most during 2nd week = cm height.

During which week did Plant B grow least?

** Answer: **

(f) The week in which Plant B grow least is during first week =

Were the two plants of the same height during any week shown here? Specify.

** Answer: **

(g) At the end of second week, heights of both plants are same.

** Answer: **

(a) The forecast temperature is the same as the actual temperature on Tuesday, Friday and Sunday.

** Question:4(b) ** The following graph shows the temperature forecast and the actual temperature for each day of a week.

What was the maximum forecast temperature during the week?

** Answer: **

(b) The maximum forecast temperature during the week was on sunday.

** Question:4(c) ** The following graph shows the temperature forecast and the actual temperature for each day of a week .

What was the minimum actual temperature during the week ?

** Answer: **

(c) The minimum actual temperature during the week is .

** Question:4(d) ** The following graph shows the temperature forecast and the actual temperature for each day of a week .

On which day did the actual temperature differ the most from the forecast temperature ?

** Answer: **

(d) The actual temperature differs the most from the forecast temperature on Thursday.

** Question:5(a) ** Use the tables below to draw linear graphs.

The number of days a hill side city received snow in different years.

** Answer: **

(a) The linear graph of data given above is as shown :

** Question:5(b) ** Use the tables below to draw linear graphs.

Population (in thousands) of men and women in a village in different years.

** Answer: **

(b) The graph of data given above is as shown :

Taking years as x-axis and population as y- axis.

** Answer: **

(a) The scale taken for the time axis (x-axis) is 4 units = 1 hour.

How much time did the person take for the travel ?

** Answer: **

(b) The person travels from 8 a.m. to 11:30 a.m.

the person travels hours.

How far is the place of the merchant from the town ?

** Answer: **

(c) The place of the merchant from the town is 22 km away.

Did the person stop on his way? Explain.

** Answer: **

(d) From 10 a.m. to 10:30 a.m. ,there is a horizontal line which states that person stops from 10 a.m. to 10:30 a.m.

During which period did he ride fastest ?

** Answer: **

(e) From graph we can observe person travels maximum distance from 8 a.m. to 9 a.m.

Hence,person travels fastest from 8 a.m. to 9 a.m.

** Question:7(i) ** Can there be a time-temperature graph as follows? Justify your answer.

** Answer: **

(i) Yes, there can be a time-temperature graph as shown with the increase in time, temperature also increases.

** Question:7(ii) ** Can there be a time-temperature graph as follows? Justify your answer.

** Answer: **

(ii) Yes, it is possible that with increase in time temperature decreases.

** Question:7(iii) ** Can there be a time-temperature graph as follows? Justify your answer.

** Answer: **

(iii) No,this type of graph is not possible because different temperature at same time are not posiible.

** Question:7(iv) ** Can there be a time-temperature graph as follows? Justify your answer

** Answer: **

(iv) Yes, it is possible i.e. same temperature at different time is possible.

** NCERT solutions for class 8 maths chapter 15 introduction to graphs-Exercise: 15.2 **

** Question:1(i) ** Plot the following points on a graph sheet. Verify if they lie on a line

A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

** Answer: **

(a) A(4, 0), B(4, 2), C(4, 6), D(4, 2.5)

** Question:1(b) ** Plot the following points on a graph sheet. Verify if they lie on a line

P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

** Answer: **

(b) P(1, 1), Q(2, 2), R(3, 3), S(4, 4)

The graph is as shown :

** Question:1(c) ** Plot the following points on a graph sheet. Verify if they lie on a line

K(2, 3), L(5, 3), M(5, 5), N(2, 5)

** Answer: **

(iii) K(2, 3), L(5, 3), M(5, 5), N(2, 5)

The graph is as shown :

** Answer: **

As shown below is graph :

The coordinates of the points at which this line meets the x-axis and y-axis are

** Question:3 ** Write the coordinates of the vertices of each of these adjoining figures.

** Answer: **

The coordinates of vertices are:

, , ,

, , ,

, ,

** Question:4(i) ** State whether True or False. Correct that are false.

A point whose x coordinate is zero and y-coordinate is non-zero will

lie on the y-axis .

** Answer: **

(i) True .A point whose x coordinate is zero and y-coordinate is non-zero will

lie on the y-axis. = here, y is variable.

** Question:4(ii) ** State whether True or False. Correct that are false.

A point whose y coordinate is zero and x-coordinate is 5 will lie on y-axis.

** Answer: **

(ii) False.Point does not lie on y-axis.A point whose y coordinate is zero and x-coordinate is 5 will not lie on

y-axis.

** Question:4(iii) ** State whether True or False. Correct that are false.

The coordinates of the origin are (0, 0).

** Answer: **

(iii)True. The coordinates of the origin are (0, 0).

** NCERT solutions for class 8 maths chapter 15 introduction to graphs topic 15.3 some applications **

** Question:1 ** In the above example, use the graph to find how much petrol can be purchased for Rs 800.

** Answer: **

From the graph given below we can say that for Rs 800 we can buy 16 litres.

** Answer: **

Taking a case of direct variation the graph is as shown below.

Taking sum deposite as 100,200,300,500 ,1000.

and 10% Simple Interest (S.I.).

** NCERT solutions for class 8 maths chapter 15 Introduction to Graphs-Exercise: 15.3 **

** Question:1(a) ** Draw the graphs for the following tables of values, with suitable scales on the axes.

Cost of apples

** Answer: **

(a) Cost of apples

** Question:1(b) ** Draw the graphs for the following tables of values, with suitable scales on the axes . Distance travelled by a car.

(i)How much distance did the car cover during the period 7.30 a.m. to 8 a.m?

** Answer: **

(b)

(i)From the above graph,the distance the car cover during the period 7.30 a.m. to 8 a.m is

** Question:1(b) ** Draw the graphs for the following tables of values, with suitable scales on the axe.

(ii) What was the time when the car had covered a distance of 100 km since it’s star

** Answer: **

(b)

(ii)From above graph we conclude that at 7:30 a.m., the car had covered a distance of 100 km since it’s start.

** Question:1(c) ** Interest on deposits for a year .

(i) Does the graph pass through the origin?

** Answer: **

(c)

Taking x axis as 1000 units = 1 box and y axis as 100 units = 1 box.

(i)Yes, the graph pass through the origion.

** Question:1(c) ** Interest on deposits for a year

(ii) Use the graph to find the interest on Rs 2500 for a year.

** Answer: **

(c)

(ii) Using the graph, the interest on Rs 2500 for a year is Rs 200.

** Question:1(c) ** Interest on deposits for a year .

(iii) To get an interest of Rs 280 per year how much money should be deposited ?

** Answer: **

(iii) From the graph,to get an interest of Rs 280 per year Rs 3500 money should be deposited.

** Question:2(i) ** Draw a graph for the following Is it a linear graph

** Answer: **

From the above graph ,we conclude that graph is linear.

** Question:2(ii) ** Draw a graph for the following

** Answer: **

From above graph,we conclude that graph is not linear.

** NCERT solutions for class 8 maths: Chapter-wise **

** NCERT solutions for class 8: Subject-wise **

** Benefits of NCERT solutions for class 8 maths chapter 15 introduction to graphs- **

- You will get to know the different applications of the graph based on the need and given data.
- It will help you in your homework as all the practice questions including questions given below every topic are covered in this article.
- You can predict future events with the help of graphs using data of past events.
- You will also get solutions to the practice questions given below every topic which will give you conceptual clarity.
- You should draw the graphs given in the NCERT textbook. You can take help from the NCERT solutions for class 8 maths chapter 15 introduction to graphs.

** Happy learning!!! **

## Frequently Asked Question (FAQs) - NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

**Question: **What are the important topics of chapter Introduction to Graphs ?

**Answer: **

Bar graph, Pie graph, histogram, line graph, linear graphs, location of a point on graph, coordinates, and some applications of graphs are covered in this chapter.

**Question: **How does the NCERT solutions are helpful ?

**Answer: **

NCERT solutions are provided in a very detailed manner which will give conceptual clarity to the students. Also, they can take help from solutions if they are not able to solve NCERT problems on their own.

**Question: **Where can I find the complete solutions of NCERT for class 8 ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 by clicking on the link.

**Question: **Where can I find the complete solutions of NCERT for class 8 maths ?

**Answer: **

Here you will get the detailed NCERT solutions for class 8 maths by clicking on the link.

**Question: **How many chapters are there in the CBSE class 8 maths ?

**Answer: **

There are 16 chapters starting from rational number to playing with numbers in the CBSE class 8 maths.

**Question: **Which is the official website of NCERT ?

**Answer: **

NCERT official is the official website of the NCERT where you can get NCERT textbooks and syllabus from class 1 to 12.

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