NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs

# 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.

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 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

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

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

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

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

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

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

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

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

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

(a) The sales in

(1) 2002 = 4 crore

(2) 2006 = 8 crore

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

(b) The sales in

(1) 2003 = 7 crore

(2) 2005 = 10 crore

Compute the difference between sales in 2002 and 2006

(c) The difference between sales in 2002 and 2006 $=8-4 =4$ .

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

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

(a) The Plant A after

(i) 2 weeks = 7 cm height.

(ii) 3 weeks = 9 cm height.

(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?

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

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

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

During which week did Plant A grow most?

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

During which week did Plant B grow least?

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

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

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

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

What was the maximum forecast temperature during the week?

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

What was the minimum actual temperature during the week ?

(c) The minimum actual temperature during the week is $15 \degree\:C$ .

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

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

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

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

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

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

(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 ?

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

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

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

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

Did the person stop on his way? Explain.

(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 ?

(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.

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

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

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

(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

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

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

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

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

The graph is as shown :

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

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

The graph is as shown :

As shown below is the graph :

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

The coordinates of vertices are:

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

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

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

(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.

(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).

(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

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

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.).

Class 8 introduction to graphs NCERT solutions - Exercise: 15.3

(a) Cost of apples

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

(b)

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

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

(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?

(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.

(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 ?

(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

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.

## 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.
• 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

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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Get answers from students and experts

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

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