# 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.

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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 Classes 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.

** 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 A grow during the 3rd week?

** Answer: **

(c)The Plant A grow during the 3rd week =

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 the 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.

** Introduction to Graphs Class 8 Math Chapter 15-Topics **

- A Bar graph
- A Pie graph (or a circle-graph)
- A histogram
- A line graph
- Linear Graphs
- Location of a point
- Coordinates
- Some Applications

** **NCERT Solutions for Class 8 Maths: Chapter-Wise

Chapter -1 | |

Chapter -2 | |

Chapter-3 | |

Chapter-4 | |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | Introduction to Graphs |

Chapter-16 |

### 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!!! **

**Also Check NCERT Books and NCERT Syllabus here:**

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

**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.

**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: **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: **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: **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: **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.

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