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NCERT Solutions for Class 8 Maths Chapter 15 - Introduction To Graphs

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Last updated date: 22nd Mar 2024
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MVSAT 2024

NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs - Free PDF Download

Graphs are introduced as a part of the math curriculum in schools. Charts assist students in arranging and examining information logically and making it easier for the students to explain data. Line graphs allow an easy and visible way for the students of all standards to review the information and extract conclusions about mathematical relationships.


Class:

NCERT Solutions For Class 8

Subject:

Class 8 Maths

Chapter Name:

Chapter 15 - Introduction to Graphs

Content Type:

Text, Videos, Images and PDF Format

Academic Year:

2023-24

Medium:

English and Hindi

Available Materials:

  • Chapter Wise

  • Exercise Wise

Other Materials

  • Important Questions

  • Revision Notes


Students are introduced to graphs from NCERT solutions of class 8 maths chapter 15. Line graphs include:

  • Grouping

  • More than 

  • Equality

  • Inequality

  • Less than


Students are also aware of the fact that graphs have limits. They do not illustrate all of the information and do not consider any alternate options. With a pictorial graph or a pie chart, students can quickly find a solution. Download free NCERT Solution PDF on vedantu website. Register online for NCERT Solutions for Class 8 Science tuitions which are curated by our expert master teachers.


Important Topics under NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

Chapter 15 of the Class 8 maths syllabus is Introduction to Graphs. This is an essential chapter covered in the syllabus. The NCERT Solutions for Class 8 Maths Chapter 15 encapsulates all the necessary information required to solve and practise the sums given in this chapter. This chapter has 4 major sections or topics. The following are the major topics that come under the chapter Introduction to Graphs. Going through these topics will ensure easy understanding and practice of the sums covered in this chapter.

  • Types of Graphs in Mathematics

  • Explanation of Different Graphs

  • Questions on Graphical Representation

  • Some Solutions to Graphical Equations

Our advice to the students is that they read through every topic carefully and then solve and practise the NCERT Solutions for Class 8 Maths Ch 15 Introduction to Graphs.

Access NCERT solutions for Maths Chapter 15 – Introduction to Graphs (Examples, Easy Methods and Step by Step Solutions)

Exercise 15.1 

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

(a) What was the patient’s temperature at 1 p.m.? 

(b) When was the patient’s temperature 38.5°C? 

(c) The patient’s temperature was the same two times during the period given. What were these two times? 

(d) What was the temperature at 1.30 p.m? How did you arrive at your answer? 

(e) During which periods did the patient’s temperature show an upward trend?


Graph ( temperature vs time)


Graph ( temperature vs time), Image Credits-NCERT


Ans: (a) The patient's temperature was $36.5{}^\circ C$at $1$ p.m.

(b) At $12$ p.m., the patient's temperature was $38.5{}^\circ C$.

(c) At 1 p.m. and 2 p.m., the patient's temperature was the same.

(d) The graph between $1$ and $2$ p.m. is parallel to the x-axis. At $1$ p.m. and $2$ p.m., the temperature is $36.5{}^\circ C$. So, $1:30$p.m., the temperature is $36.5{}^\circ C$.

(e) The patient's temperature showed an upward trend in the following periods.


$9$ a.m. to $10$ a.m., $10$ a.m. to $11$ a.m., $2$ p.m. to $3$ p.m.


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

(a) What were the sales in (i) $2002$ (ii) $2006$? 

(b) What were the sales in (i) $2003$ (ii) $2005$? 

(c) Compute the difference between the sales in $2002$ and $2006$. 

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


Graph Sales ( in Rs crores ) Vs Years

  

Graph Sales ( in Rs crores ) Vs Years, Image Credits-NCERT

Ans: (a) 

(i)The sales in $2002$ were Rs $4$crores.

(ii)The sales in $2006$ were Rs $8$crores.


(b)

(i)The sales in $2003$ were Rs $7$crores.

(ii)The sales in $2005$ were Rs $10$crores.


(c)Difference between the sales in $2002$ and $2006$

= Rs ($8$ − $4$) crores

 = Rs $4$ crores 


(d)Difference between the sales in $2006$ and $2005$

= Rs ($10$ − $8$) crores

 = Rs $2$ crores 


Difference between the sales in $2005$ and $2004$

= Rs ($10$ − $6$) crores

 = Rs $4$ crores 


Difference between the sales in $2004$ and $2003$

= Rs ($7$ − $6$) crores

 = Rs $1$ crores 


Difference between the sales in $2003$ and $2002$

= Rs ($7$ − $4$) crores

 = Rs $3$ crores 


As a result, the difference was greatest in $2005$ as compared to the prior year, $2004$.


3: 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. 

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

(b) How high was Plant B after (i) $2$ weeks (ii) $3$weeks? 

(c) How much did Plant A grow during the $3rd$ week?

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

(e) During which week did Plant A grow most? 

(f) During which week did Plant B grow least? 

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


Graph Height ( in cm ) Vs Weeks


Graph Height ( in cm ) Vs Weeks, Image Credits-NCERT


Ans: (a) (i)Plant A had grown to a height of $7$ cm after two weeks.

(ii) Plant A grew to a height of $9$ cm after three weeks.


(b) Plant B grew to a height of $7$ cm after two weeks.

(ii) Plant B grew to a height of $10$ cm after three weeks.


(c)Plant A's growth during the third week = $9-7$ 

= $2$cm


(d)Plant B's growth from the end of the second to the end of the third week 

=$10-7$ 

= $3$cm


(e) Plant A's growth over the first week = $2-0$ 

= $2$cm

Plant A's growth over the second week = $7-2$

= $5$cm

Plant A's growth during the third week = $9-7$

= $2$cm

As a result, during the second week, plant A grew the most, gaining $5$cm.


(f)Plant B's growth over the first week = $1-0$ 

= $1$cm

Plant B's growth over the second week = $7-1$

= $6$cm

Plant B's growth during the third week = $10-7$

= $3$cm

As a result, during the first week, plant B grew the least i.e. $1$cm.


(g)The heights of both plants were the same at the conclusion of the second week.

 

4: The following graph shows the temperature forecast and the actual temperature for each day of a week. 

(a) On which days was the forecast temperature the same as the actual temperature? 

(b) What was the maximum forecast temperature during the week? 

(c) What was the minimum actual temperature during the week? 

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


Graph Temperature  Vs Day


Graph Temperature  Vs Days, Image Credits-NCERT


Ans: (a) On Tuesday, Friday, and Sunday, the forecast temperature matched the actual temperature.

(b)The maximum forecast temperature during the week was $35{}^\circ C$. 

(c) The minimum actual temperature during the week was $15{}^\circ C$.

(d)On Thursday, the actual temperature differs the most from the forecast temperature. 


5. Use the tables below to draw linear graphs. 

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


Year

$2003$

$2004$

$2005$

$2006$

Days

$8$

$10$

$5$

$12$


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


Year

$2003$

$2004$

$2005$

$2006$

$2007$

Number of men  

$12$

$12.5$

$13$

$13.2$

$13.5$

Number of women  

$11.3$

$11.9$

$13$

$13.6$

$12.8$


Ans:(a)

The linear graph of the given information can be constructed using the years on the x-axis and the number of days on the y-axis, with scales of $1$ unit = $2$ days on the y-axis and $2$unit = $1$ year on the x-axis. 


Graph Days  Vs Years


Graph Days  Vs Years


(b)

The linear graph of the given information may be constructed by plotting the years on the x-axis and the population on the y-axis, with scales of $1$ unit = $0.5$ thousand on the y-axis and $2$ unit = $1$ year on the x-axis.


Graph Population(in thousand) Vs Years
 


Graph Population(in thousand) Vs Years


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


Graph Distance (in km)  Vs Time


Graph Distance (in km)  Vs Time, Image Credits-NCERT


(a) What is the scale taken for the time axis? 

(b) How much time did the person take for the travel? 

(c) How far is the place of the merchant from the town? 

(d) Did the person stop on his way? Explain. 

(e) During which period did he ride fastest? 


Ans:

(a) Scale taken for the time axis is $4$ units = $1$ hour
(b) The person travelled between the hours of $8$ a.m. and $11:30$ a.m. As a result, the guy had to travel for $3\frac{1}{2}$  hours. 

(c) The merchant is $22$ kilometres away from town. 

(d) Yes, from $10$a.m. to $10:30$ a.m., the person came to a halt. 

The graph's horizontal portion indicates this. 

(e) The graph shows that the person travelled the greatest distance between the hours of $8$ a.m. and $9$ a.m. 

As a result, the person's ride was the quickest between $8$ and $9$a.m. 


 7: Can there be a time temperature graph as follows? Justify you’re answer: 


Graph Temperature Vs Time


Graph Temperature Vs Time, Image Credits-NCERT


Ans:(i)This might be a time−temperature graph, as the temperature rises with the passage of time. 

(ii) This might be a time−temperature graph, as the temperature can drop as time passes. 

(iii) This isn't a time−temperature graph because it's impossible to have various temperatures at the same time. 

(iv) This can be a time−temperature graph, as the same temperature can be found at different times. 


Exercise 15.2

1. Plot the following points on a graph sheet. Verify if they lie on a line  

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

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

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


Ans: (a)On graph paper, we can plot the given points and join the consecutive points as follows. 


Position of Points A, B, C and D


Position of Points A, B, C and D


The points A, B, C, and D all lie on the same line, as can be seen in the graph.


(b)On graph paper, we can plot the given points and join the consecutive points as follows. 


Position of Points P, Q, R and S


Position of Points P, Q, R and S

As a result, the points P, Q, R, and S are all on the same line.


(c)On graph paper, we can plot the given points and join the consecutive points as follows.


Position of Points K, L,M and N
 


Position of Points K, L,M and N


As a result, the points K, L, M, and N are not on the same line. 


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. 


Ans:


Line Passing through Points (2, 3) and (3, 2


Line Passing through Points (2, 3) and (3, 2)


The line connecting the points $(2,3)$ and $(3,2)$ intersects the x-axis at point $(5,0)$ and the y-axis at point $(0,5)$ on the graph .


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


Different Shapes Formed by Points

Different Shapes Formed by Points, Image Credits-NCERT


Ans: The coordinates of the vertices in the given figure are as follows. 

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

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

K $(10,5)$, L $(7,7)$, M $(10,8)$   


4: State whether True or False. Correct those are false. 

(i) A point whose x coordinate is zero and y-coordinate is non-zero will lie on the yaxis. 

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

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


Ans: (i) True 

(ii) False , it will lie on x-axis. 

(iii) True   


Exercise 15.3 

1:Draw the graphs for the following tables of values, with suitable scales on the axes. 

(a) Cost of apples 


Number of apples

$1$

$2$

$3$

$4$

$5$

Cost(in Rs)

$5$

$10$

$15$

$20$

$25$


(b) Distance travelled by a car 


Time(in hours)

$6a.m.$

$7a.m.$

$8a.m.$

$9a.m.$

Distance(in km)

$40$

$80$

$120$

$160$


(i) How much distance did the car cover during the period $7:30$  a.m. to $8$ a.m.?$$ 

(ii) What was the time when the car had covered a distance of $100$ km since its start?

(c) Interest on deposits for a year: 


Deposit(in Rs)

$1000$

$2000$

$3000$

$4000$

$5000$

Simple interest (in Rs)

$80$

$160$

$240$

$320$

$400$


(i) Does the graph pass through the origin? 

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

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


Ans: (a)  We may mark the quantity of apples on the x-axis and the cost of apples on the y-axis using a suitable scale ($1$ unit = $1$ apple on the x-axis and $1$unit = Rs $5$ on the y-axis).


The following is a graph of the given data.


Graph Cost(Rs) Vs Number of Apples


Graph Cost(Rs) Vs Number of Apples


(b) Using a suitable scale ($2$ units = $1$ hour on the x-axis and $2$ units = $40$ kilometres on the y-axis), we can display the time on the x-axis and the distance travelled by the car on the y-axis.


The following is a graph of the given data.


Graph Distance (km) Vs Time (hours)


Graph Distance (km) Vs Time (hours)


(i) The car covered a distance of $20$ kilometres between $7:30$ a.m. and $8$ a.m.

(ii) At $7:30$ a.m., the car had travelled $100$ kilometres since it began.


c) Selecting an appropriate scale

$1$ unit equals Rs $1000$ on the x-axis and Rs $80$ on the y-axis.

On the x-axis, we can represent the deposit, and on the y-axis, we can indicate the interest earned on that account.

The following is a graph of the given data. 


Graph Simple Interest Vs Deposit (Rs)


Graph Simple Interest Vs Deposit (Rs)


From the graph, the following points can be observed. 

(i) Yes. The graph passes through the origin. 

(ii) The interest earned in a year on a deposit of Rs $2500$ is Rs $200$. 

(iii) To get an interest of Rs $280$ per year, Rs $3500$ should be deposited. 


2:Draw a graph for the following. 

(i) 


Side of square(in cm)

$2$

$3$

$3.5$

$5$

$6$

Perimeter

$8$

$12$

$14$

$20$

$24$


Is it a linear graph? 


Side of square(in cm)

$2$

$3$

$4$

$5$

$6$

Area(in cm2)

$4$

$9$

$16$

$25$

$36$


Is it a linear graph? 

Ans:(i)Selecting an appropriate scale

$1$ unit equals $1$ cm on the x-axis and $4$ cm on the y-axis.

On the x-axis, we may represent a square's side, and on the y-axis, we can represent the square's perimeter.

The following is a graph of the given data.

 

Graph Perimeter (cm) Vs Side of Square (cm)


Graph Perimeter (cm) Vs Side of Square (cm)


It is a linear graph.

(ii)Selecting an appropriate scale

$1$ unit = $1$ cm on the x-axis and $4$ cm2 on the y-axis

On the x-axis, we may indicate the side of a square, and on the y-axis, we can represent the area of that square.


Graph Area (square meter) Vs Side of Square (cm)


Graph Area (square meter) Vs Side of Square (cm)


The following is a graph of the given data. It is not a linear graph.

Class 8 Maths Chapter 15 Introduction to Graphs NCERT Solutions - PDF Download

Among different vital chapters in class 8th standard, graphical introduction in class 8 chapter 15 maths helps students evolve the idea of critical thinking and find solutions methodically. Apart from learning visual representation, students can go through several vital chapters like:

  • Linear Equations in One Variable

  • Data Handling

  • Exponents and Powers

  • Mensuration

  • Factorisation

  • Comparing Quantities

  • Squares and Square Roots

  • Understanding Quadrilaterals

  • Rational Numbers

 

NCERT solution for class 8 maths chapter 15 provides different solutions to complicated mathematical problems, regardless of the classes, and also includes maths NCERT solutions class 8 chapter 15. 

 

Class 8 Maths Chapter 15 Includes:

Chapter 15 Introduction to Graphics All Exercises in PDF Format

Exercise 15.1

7 Question and Solutions

Exercise 15.2

4 Questions and Solutions

Exercise 15.3

2 Questions and Solutions


Types of Graphs in Mathematics

While chapter 15 class 8 maths explains fundamental concepts of graphs, its solutions provide answers to the in-text questionnaire. There are different divisions of charts, and each graphical division is utilised in separate chapters. 

 

Explanation of Different Graphs

Different graphs have different functions to perform in class 8 maths chapter 15. The procedures of different graphs are explained below:

  • A Bar Graph shows a contrast between classifications. It may consist of rectangles, parallel, vertical and horizontal bars.

  • Pie Graphs, also called Circle Graph, compares a whole part.

  • Histogram shows data in intervals, and it consists of adjacent bars over the intervals.

  • Line Graphs presents data that get modified constantly over a while.

 

Questions on Graphical Representation

Students are provided with graphical knowledge from NCERT class 8 maths chapter 15 solutions. Some questions solved by visual representation are explained below:

The above graphical chart displays a patient's temperature in a hospital, which has been noted down every hour. The probable questions that students can find in NCERT maths class 8 chapter 15 are listed below:

  • Patient’s temperature at 1.00 pm?

  • What was the patient’s temperature at 1.30 pm?

  • In which period, the patient showed a growing trend?

  • What were those two times when the patient’s temperature was the same during the given period?

After thoroughly studying the graph, students can quickly answer these questions. Students willing to know more about graphical representation from NCERT class 8 maths chapter 15 solutions can download Vedantu’s official app and get access to free PDF for online courses.

 

Some Solutions to Graphical Equations

It is needless to say how the graphical representation clears the students' concept and teaches them to save time and effort by using graphs to solve a mathematical equation. A graphical representation quickly grabs students’ attention and induces interest among them. There are few solutions below which can help students understand how graphic representation functions in maths NCERT class 8 chapter 15.


Students can have a precise idea about how to do calculations through graphical charts. To learn more, interested students can visit the official website of Vedantu and get overall guidance regarding class 8 maths chapter 15 solutions. Have  a look at exercise 15.1 , exercise 15.2, and exercise 15.3 to cover all the syllabus for exam preparation.


In the end, it is to be remembered that graphical representation associated with chapter 15 class 8 maths is an essential help for students preparing for exams and assignments.

Benefits of Using Vedantu for Class 8 Maths Chapter 15 - Introduction to Graphs

Key Features of NCERT Solutions, These solutions are designed to help students achieve proficiency in their studies. They are crafted by experienced educators who excel in teaching class 8 Maths. Some of the features include:


  • Comprehensive explanations for each exercise and questions, promoting a deeper understanding of the subject.

  • Clear and structured presentation for easy comprehension.

  • Accurate answers aligned with the curriculum, boosting students' confidence in their knowledge.

  • Visual aids like diagrams and illustrations to simplify complex concepts.

  • Additional tips and insights to enhance students' performance.

  • Chapter summaries for quick revision.

  • Online accessibility and downloadable resources for flexible study and revision.


Conclusion

The NCERT Solutions for Class 8 Maths Chapter 15 - Introduction to Graphs, provided by Vedantu, is a valuable tool for Class 8 students. It helps introduce Maths concepts in an accessible manner. The provided solutions and explanations simplify complex ideas, making it easier for Class 8 Students to understand the material. By using Vedantu's resources, Students can develop a deeper understanding of NCERT concepts. These solutions are a helpful aid for grade 8 students, empowering them to excel in their studies and develop a genuine appreciation for “Introduction to Graphs”.

FAQs on NCERT Solutions for Class 8 Maths Chapter 15 - Introduction To Graphs

1. What are the five essential things that a graph needs?

There are five important things that students should keep in mind while drawing a graph, and they are:

  • Axes and Background

  • Grid lines

  • Visual structures

  • Scales and tick marks

  • Text

2. What are the crucial elements of a useful graph?

Among different important elements, five principal features are explained below:

  • The experiment which describes the title

  • The graphical representation should fill the space allocated for the graph

  • Every data point should be arranged in a proper position

  • Each axes should be categorised with the measured quantity and the measuring units

  • A best-fitted line is required

3. What is a useful chart?

To make comparisons, Bar charts are the best option, whereas line charts are good for trends. For relationships and distribution, Scatter plot charts work better, but Pie charts are only utilised for compositions, not for any comparisons or distributions.

4. Where can I download the latest NCERT Solutions for Chapter 15 “Introduction to Graphs” of Class 8 Maths? 

To download Vedantu's NCERT Solutions for Chapter 15 of Class 8 Maths  follow these direct steps:

  • Visit the page NCERT Solutions for Chapter 15 of Class 8 Maths. 

  • Scroll down and click on the option to "Download PDF."

  • The subsequent page will open that carries the link to download the PDF automatically.

These solutions are regularly updated as per the CBSE guidelines and syllabus. Hence, these are the latest solutions you can find online. Moreover, they are available to be downloaded free of charge.

5. Does Vedantu provide answers to all the questions of Chapter 15 “Introduction to Graphs” of Class 8 Maths?

In Chapter 15  "Introduction to Graphs," there are three exercises in total. Vedantu provides detailed answers to each question of these exercises. The solutions are explained step by step with graphs wherever required.  Vedantu's NCERT Solutions for Class 8 Chapter 15 "Introduction to Graphs" provide solutions that are well suited for examinations.  These are prepared after a painstaking process by our experts and hence are reliable. Moreover, Vedantu provides additional explanations of the chapter's concepts to allow students to comprehend the chapter better. These solutions are available free of cost on the Vedantu website and the Vedantu app.

6. How many types of graphs are there in Chapter 15 “Introduction to Graphs” of Class 8 Maths?

Chapter 15 "Introduction to Graphs" teaches the students the basic types and functions of graphs. The various types of graphs introduced in this chapter are as follows:

  • Bar graphs: to compare various categorical data

  • Histograms: to represent data in intervals

  • Pie graphs: to compare parts of a whole

  • Line graphs:  to show continuous change over a certain duration

  • Linear graphs: a whole unbroken line graph

These graphs have several real-time applications, and thus students should pay close attention to this chapter.

7. How do you draw a linear graph?

To draw a linear graph, concepts of plotting points on graph paper, coordinates, and location of points must be clear in your mind.

  • Choose a suitable scale for the x and y-axis.

  • Mark the required quantities accordingly on the x and y-axis.

  • As per the quantities given in the question, plot the points on the graph.

  • Join the plotted points. This should provide you with a straight line on the graph.

8. Why do we use graphs according to Chapter 15 of Class 8 Maths?

Graphs have infinite uses in our lives. They are used for visually representing accurate data for various purposes. Such a graphical representation of collected data is convenient to comprehend.  Graphs can easily represent large quantities that might be difficult to display in text.


You might have often come across various graphs on news channels, magazines, newspapers, etc.  They can be used to depict temperature and weather changes, display annual reports, profits, losses, scores in sports, etc.