NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

Edited By Ramraj Saini | Updated on Mar 01, 2024 06:48 PM IST

Introduction to Graphs Class 8 Questions And Answers provided here. These NCERT Solutions are created by expert team at craeers360 keeping the latest syllabus and pattern of CBSE 2023-23. 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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Introduction to Graphs Class 8 Questions And Answers PDF Free Download
Introduction to Graphs Class 8 Solutions - Important Points
Introduction to Graphs Class 8 NCERT Solutions (Intext Questions and Exercise)
Class 8 maths chapter 15 NCERT solutions -Topics
NCERT Solutions for Class 8 Maths - Chapter Wise
Key Features Of Introduction To Graphs Class 8 Solutions
NCERT Solutions for Class 8 - Subject Wise
NCERT Books and NCERT Syllabus

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

Here you will get the detailed NCERT Solutions for Class 8 Maths by clicking on the link. In Introduction to Graphs class 8 solutions, 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.

Introduction to Graphs Class 8 Questions And Answers PDF Free Download

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Introduction to Graphs Class 8 Solutions - Important Points

Bar Graph: Used to compare categories or discrete data.
Pie Chart: Best for comparing sections of a whole, typically showing proportions.
Histogram: Useful for simplifying data presented in intervals, especially for frequency distributions.
Line Graph: Beneficial for data that changes continuously over time, showing trends and patterns.
Coordinates: To fix a point on a graph, both x-coordinate (horizontal) and y-coordinate (vertical) are required.
Graph: A graph depicts the relationship between a dependent variable and an independent variable, showing how changes in one variable affect the other.

Free download NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs for CBSE Exam.

Introduction to Graphs Class 8 NCERT Solutions (Intext Questions and Exercise)

NCERT Class 8 maths chapter 15 question answer - 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

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Answer:

(a) The patient's temperature at 1 p.m is $36.5 \degree$ celsius.

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

When was the patients temperature $38.5 \degree C$ ?

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Answer:

(b) The patients temperature is $38.5 \degree C$ at 12 noon.

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

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Answer:

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?

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Answer:

(d) The temperature at 1:30 p.m is $36.5\degree$ celsius. The temperature at 1 p.m. to 2 p.m. is same i.e. $36.5\degree$ celsius so it is also same as at 1:30 p.m is $36.5\degree$ 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 ?

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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 ?

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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 ?

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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

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Answer:

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 ?

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Answer:

(d) The greatest difference between the sales as compared to its previous year is $10-6=4 crores$ between 2004 and 2005.

Question:3(a) For an experiment in Botany , two different plants plant A and plant B were grown under similar laboratory conditions Their heights were measured at the end of each week for 3 weeks The result are shown by the following graph

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

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Answer:

(a) The Plant A after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 9 cm height.

Question:3(b) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.
How high was Plant B after (i) 2 weeks (ii) 3 weeks?

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Answer:

(b) The Plant B after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 10cm height.

Question:3(c) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

How much did Plant A grow during the 3rd week?

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Answer:

(c)The Plant A grow during the 3rd week = $9-7 = 2\, \, cm$

Question:3(d) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

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

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Answer:

(d)The Plant B grow from the end of the 2nd week to the end of the 3rd week $10-7=3 cm$ height.

Question:3(e) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

During which week did Plant A grow most?

154499

Answer:

(e)The week in which Plant A grow most during 2nd week = $7-2=5$ cm height.

Question:3(f) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

During which week did Plant B grow least?

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Answer:

(f) The week in which Plant B grow least is during first week = $1-0=1cm$

Question:3(g) For an experiment in Botany, two different plants, plant A and plant B were grown under similar laboratory conditions. Their heights were measured at the end of each week for 3 weeks. The results are shown by the following graph.

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

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Answer:

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

Question:4(a) The following graph shows the temperature forecast and the actual temperature for each day of a week.
On which days was the forecast temperature the same as the actual temperature?

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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?

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Answer:

(b) The maximum forecast temperature during the week was $35 \degree\:C$ 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 ?

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Answer:

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 ?

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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.

1643872740500 Answer:

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

1643872765090

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

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

1643872786741

Answer:

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

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

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Question:6(a) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.
What is the scale taken for the time axis?

1444

Answer:

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

Question:6(b) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph.

How much time did the person take for the travel ?

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Answer:

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

$\therefore$ the person travels $3\frac{1}{2}$ hours.

Question:6(c) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant .His distance from the town at different times is shown by the following graph .

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

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Answer:

Question:6(d) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant . His distance from the town at different times is shown by the following graph.

Did the person stop on his way? Explain.

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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.

Question:6(e) A courier-person cycles from a town to a neighbouring suburban area to deliver a parcel to a merchant .His distance from the town at different times is shown by the following graph .

During which period did he ride fastest ?

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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.

122

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.

12223

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.

122265

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

12355

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)

1643872810396

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 :

1643872827875

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 : 1643872852014

Question:2 Draw the line passing through (2, 3) and (3, 2). Find the coordinates of the points at
which this line meets the x-axis and y-axis.

Answer:

As shown below is the graph :

1643872881870 The coordinates of the points at which this line meets the x-axis and y-axis are $(5,0) and (0,5)$

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

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Answer:

1355444

The coordinates of vertices are:

$O(0,0)$ , $A(2,0)$ $B(2,3)$ , $C(0,3)$ ,

$P(4,3)$ , $Q(6,1)$ , $R(6,5)$ , $S(4,7)$

$L(7,7)$ , $M(10,8)$ , $K(10,5)$

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. = $(0,y)$ 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 $(5,0)$ 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.

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Answer:

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

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Question:2 A bank gives 10% Simple Interest (S.I.) on deposits by senior citizens. Draw a graph to illustrate the relation between the sum deposited and simple interest earned. Find from your graph Try a case of direct variation?

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.).

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Class 8 introduction to graphs NCERT solutions - 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

1222222

1643872920439

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?

1643872944334 Answer:

(b) 1643872965950

(i)From the above graph,the distance the car cover during the period 7.30 a.m. to 8 a.m is $120-100=20 km.$

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

Distance travelled by a car. 1643872992889

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

Answer:

(b)

1643873027182

(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.

1643873052963

(i) Does the graph pass through the origin?

Answer:

(c)

1643873070973

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

1643873104733

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

Answer:

(c)

1643873130396

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

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

1643873154934 (iii) To get an interest of Rs 280 per year how much money should be deposited ?

Answer:

1643873189477

(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: 1643873217958

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

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

Is it a linear graph?

Answer: 1643873248491 From above graph,we conclude that graph is not linear.

Class 8 maths chapter 15 NCERT solutions -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	Rational Numbers
Chapter -2	Linear Equations in One Variable
Chapter-3	Understanding Quadrilaterals
Chapter-4	Practical Geometry
Chapter-5	Data Handling
Chapter-6	Squares and Square Roots
Chapter-7	Cubes and Cube Roots
Chapter-8	Comparing Quantities
Chapter-9	Algebraic Expressions and Identities
Chapter-10	Visualizing Solid Shapes
Chapter-11	Mensuration
Chapter-12	Exponents and Powers
Chapter-13	Direct and Inverse Proportions
Chapter-14	Factorization
Chapter-15	Introduction to Graphs
Chapter-16	Playing with Numbers

Key Features Of Introduction To Graphs Class 8 Solutions

Comprehensive Coverage: Maths chapter 15 class 8 solutions cover all topics and concepts related to graph representations and interpretations as per the Class 8 syllabus.

Step-by-Step Solutions: Class 8 maths ch 15 question answer are detailed, step-by-step explanations for each problem, making it easy for students to understand and apply mathematical concepts related to graphs.

Variety of Problems: A wide range of problems, including exercises and additional questions, to help students practice and test their understanding of graphical representations.

NCERT Solutions for Class 8 - Subject Wise

NCERT Solutions for Class 8 Maths chapter 15 Introduction to Graphs - Benefits

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.

NCERT Books and NCERT Syllabus

Frequently Asked Questions (FAQs)

1. What are the important topics of ch 15 maths class 8 Introduction to Graphs ?

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.

2. How does the NCERT solutions are helpful ?

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.

3. Where can I find the complete solutions of NCERT for class 8 ?

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

4. Where can I find the complete solutions of NCERT for class 8 maths ?

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

5. How many chapters are there in the CBSE class 8 maths ?

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

6. Which is the official website of NCERT ?

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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Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

Option 1) less than 3	Option 2) more than 3 but less than 6
Option 3) more than 6 but less than 9	Option 4) more than 9

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

Introduction to Graphs Class 8 Questions And Answers PDF Free Download

Introduction to Graphs Class 8 Solutions - Important Points

Introduction to Graphs Class 8 NCERT Solutions (Intext Questions and Exercise)

Class 8 maths chapter 15 NCERT solutions -Topics

NCERT Solutions for Class 8 Maths - Chapter Wise

Key Features Of Introduction To Graphs Class 8 Solutions

NCERT Solutions for Class 8 - Subject Wise

NCERT Books and NCERT Syllabus

Frequently Asked Questions (FAQs)

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