NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs

Introduction to Graphs is the thirteenth chapter of Class 8 NCERT Maths. This chapter comprehensively covers essential topics such as Introduction and Some Applications. By mastering these topics, students will strengthen their foundational knowledge of mathematics. The NCERT Solutions for Class 8 Maths Chapter 13 provides clear, step-by-step guidance, helping students tackle complex problems with ease and improve their overall mathematical skills. 

1.0Download Class 8 Maths Chapter 13 NCERT Solutions PDF Online

This article provides NCERT Solutions for Class 8 Introduction to Graphs, designed to help students build a solid mathematical foundation and improve their problem-solving skills. By practising these solutions, students can gain a deeper understanding of the concepts and enhance their performance in exams, leading to better scores. For comprehensive guidance, students can download the NCERT Class 8 Maths Chapter 13 PDF, meticulously curated by ALLEN’s experts, from the link below.

2.0Class 8 Maths Chapter 13 Introduction to Graphs Overview

Before discussing the specifics of NCERT Solutions for Class 8 Maths Chapter 13 Introduction to Graphs, let's quickly review the key topics and subtopics included in this chapter of the NCERT Class 8 Maths book.

Topics covered in this chapter

1. Introduction
2. Some Applications

3.0NCERT Solutions for Class 8 Maths Chapter 13 : All Exercises

4.0NCERT Questions with Solutions for Class 8 Maths Chapter 13 - Detailed Solutions

Exercise: 13.1

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

• (i) What was the patient's temperature at 1 p.m.? (ii) When was the patient's temperature $38.5^{\circ }\mathrm{C}$ ? (iii) The patient's temperature was the same two times during the period given. What were these two times? (iv) What was the temperature at 1.30 p.m.? How did you arrive at your answer? (v) During which periods did the patient's temperature showed an upward trend? Sol. In the graph, we find that the time (in hours) are represented on the $x$-axis and the temperature (in ${}^{\circ }\mathrm{C}$ ) are represented on the y-axis. The temperature and time can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that : (i) The temperature of the patient at 1 pm was $36.5^{\circ }\mathrm{C}$. (ii) The temperature of the patient was $38.5^{\circ }\mathrm{C}$ at 12 noon. (iii) The temperature of the patient was same at 1 pm and 2 pm . (iv) The temperature of the patient at 1.30 pm was $36.5^{\circ }\mathrm{C}$. The point between 1 pm and 2 pm on the x -axis is equidistant from the two points showing 1 pm and 2 pm , so it will represent 1.30 pm . Similarly, the point on the $y$-axis, between $36^{\circ }\mathrm{C}$ and $37^{\circ }\mathrm{C}$ will represent $36.5^{\circ }\mathrm{C}$. (v) During the periods 9 am to $10\mathrm{am},10\mathrm{am}$ to 11 am and 2 pm to 3 pm the patient's temperature showed an upwards trend.
• The following lines graph shows the yearly sales figures for a manufacturing company. (i) What were the sales in (a) 2002 (b) 2006? (ii) What were the sales in (a) 2003 (b) 2005? (iii) Compute the difference between the sales in 2002 and 2006.

• Sol. In the graph, we find that the years are presented on the $x$-axis and the sales (in Rs. crores) on the $y$-axis. The sales at any time (year) can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (i) (a) The sales in the year 2002 is Rs. 4 crore. (b) The sales in the year 2006 is Rs. 7 crore. (ii) (a) The sales in the year 2003 is Rs. 8 crore. (b) The sales in the year 2005 is Rs. 10 crore. (iii) The difference between the sales in 2002 and $2006=$ Rs. 7 crore - Rs. 4 crore $=$ Rs. 3 crore.
• 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 weeks? (d) How much did plant B grow from the end of the 2 nd week to the end of the 3rd week? (e) During which week did Plant A grow maximum? (f) During which week did Plant B grow least? (g) Were the two plants of the same height during any week shown here? Specify. coordinates of a point. From the graph, we observe that: (a) The height of the plant A after (i) 2 weeks was 7 cm (ii) 3 weeks was 9 cm (b) The height of the plant $B$ after (i) 2 weeks was 7 cm (ii) 3 weeks was 10 cm (c) The plant A grows 2 cm during the 3rd week. (d) The plant B grows 3 cm from the end of the 2 nd week to the end of the 3 rd week. (e) The plant A grows most during second week. (f) The plant B grows most during first week. (g) At the end of the 2nd week the heights of the two plants were the same.
• The following graph shows the temperature forecase 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

• Sol. In the graph, we find that the days are represented on the $x$-axis and the temperature forecast/ actual $\left({}^{\circ }\mathrm{C}\right)$ on the y -axis. The temperature on any day can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (a) The days on which the forecast temperature was the same as the actual temperature are Tuesday, Friday and Sunday. (b) The maximum forecast temperature during the week was $35^{\circ }\mathrm{C}$. (c) The minimum actual temperature during the week was $15^{\circ }\mathrm{C}$. (d) The actual temperature differed the most from the forecast temperature on Thursday.
• Use the tables below to draw linear graphs. (a) The number of days a hill side city received snow in different years.

Sol. (a) In order to draw the required graph, we represent years on the x-axis and the days on the y -axis. We first plot the ordered pairs (2003, 8), (2004, 10), $(2005,5)$ and $(2006,12)$ as points and then join them by line segments as shown below :

(b) In order to draw the required graph, we represent years on the x -axis and the population (in thousands) on the $y$-axis. The dotted line shows the population (in thousands) of men and the solid line shows the population (in thousands) of women.

We first plot the ordered pairs $(2003,12)$, $(2004,12.5),(2005,13),(2006,13.2)$ and $(2007,13.5)$ and then join them by the dotted line as shown, to get the graph representing the number of men. Further, we plot $(2003,11.3),(2004,11.9),(2005$, $13)$, $(2006,13.6)$ and $(2007,12.8)$ and to get the graph representing the graph of number of women. Thus, the required graph is obtained.

• A courier-person cycles from a town to a neighbouring sub-urban area to deliver a parcel to a merchant. His distance from the town at different times is shown by the following graph : (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?

• Sol. In the graph, we find that the time (in hours) is represented on the x -axis and the distance (in km) is represented on the y -axis. The distance at any time can be read from the graph exactly in the same way as we read the coordinates of a point. From the graph, we observe that: (a) The scale taken for the time axis is : 4 units = 1 hour . (b) The person took 3.5 hours for the travel. (c) The merchant's place from the town is 22 km. (d) Yes; this is indicated by the horizontal part of the graph (10 a.m. - 10.30 a.m.) (e) Between 8 a.m. and 9 a.m. he ride faster.
• Can there be a time temperature graph as follows? Justify your answer. (i)

• (ii)

• (iii)

• (iv)

• Sol. (i) This represents a time-temperature graph because it represents a smooth rise in temperature and is represented by a line graph. (ii) This represents a time-temperature graph because it represent a smooth fall in temperature and is represented by a line graph. (iii) This does not represent a timetemperature because it shows different temperatures at the same time. (iv) This represents a time-temperature graph because it shows a constant temperature at different times and is a line graph.

Exercise : 13.2

• Plot the following points on a graph sheet. Verify if they lie on a line (a) $\mathrm{A}(4,0),\mathrm{B}(4,2),\mathrm{C}(4,6),\mathrm{D}(4,2.5)$ (b) $P(1,1),Q(2,2),R(3,3),S(4,4)$ (c) $\mathrm{K}(2,3),\mathrm{L}(5,3),\mathrm{M}(5,5),\mathrm{N}(2,5)$. Sol. (a) Draw the x -axis and y -axis. Plot the points A $(4,0),B(4,2),C(4,6)$ and $D(4$, 2.5) as shown. Clearly, these points lie on a line ABDC.

• (b) Draw the x -axis and y -axis. Plot the points $P(1,1),Q(2,2),R(3,3),S(4,4)$ as shown. Clearly, these points lie on a line PQRS.

• (c) Draw the $x$-axis and $y$-axis. Plot the points $\mathrm{K}(2,3),\mathrm{L}(5,3),\mathrm{M}(5,5),\mathrm{N}(2,5)$ as shown. Clearly, these points will not lie on a line.

• 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. Sol.

• Draw the x -axis and y -axis. Plot the points $(2,3)$ and $(3,2)$. Extend the line to the axis. The extended line will meet at 5 on x -axis and 5 on $y$-axis. The coordinate are $(0,5)$ and $(5,0)$.
• Write the coordinates of the vertices of each of the figures in the graph given.

• Sol. Clearly, from the graph the coordinates of points are : $\mathrm{O}(0,0),\mathrm{A}(2,0),\mathrm{B}(2,3)$ and $\mathrm{C}(0,3)$; $P(4,3),Q(6,1),R(6,5)$ and $S(4,7)$; $\mathrm{L}(7,7),\mathrm{M}(10,8)$ and $\mathrm{K}(10,5)$.
• State whether True or False. Correct that are false. (i) A point whose $x$-coordinate is zero and $y$ coordinate is non-zero will lie on the $y$ axis. (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 $(0,0)$. Sol. (i) True. (ii) False. Correct statement is : A point whose $y$-coordinate is zero and $x$ coordinate is 5 will lie on x -axis. (iii) True.

Exercise : 13.3

• Draw the graphs for the following tables of values, with suitable scales on the axes. (a) Cost of apples

(b) Distance travelled by a car

(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 it's start? (c) Interest on deposits for a year.

(i) Does the graph pass through the origin? (ii) Use the graph to find the interest on ₹ 2500 for a year. (iii) To get an interest of ₹ 280 per year, how much money should be deposited ? Sol. (a) In order to represent the given data graphically, we represent 'Number of apples' on the x -axis and 'Cost of apples (in ₹)' on the $y$-axis. The ordered pairs $(1,5),(2,10),(3,15),(4,20)$ and $(5,25)$ are plotted as points and are joined by the line segments as shown in the figure. This gives the required graph.

Number of apples $\to$ (b)

(i) 20 km (ii) $7:30\mathrm{am}$ (c)

(i) Yes (ii) ₹ 200 (iii) ₹ 3500

• Draw a graph for the following :

(i) Is it a linear graph?

(ii) Is it a linear graph?

Sol. (i) In order to represent the given data graphically, represent the side of square (in cm ) on the x -axis and the perimeter (in cm ) on the $y$-axis. Scale : 1 unit = 1 cm on x -axis. 1 unit $=2\mathrm{cm}$ on y - axis. Plot the points $(2,8),(3,12),(3.5,14),(5$, $20)$ and $(6,24)$. Join these points to obtain the required graph. Yes, It is a linear graph.

Plot points (2, 4), (3, 9), (4, 16), $(5,25),(6$, 36) It is not a linear graph.

5.0Benefits of Studying this Chapter

1. Step-by-Step Explanations: Each solution is explained step by step, helping students follow the logic and methodology behind solving graph-related problems. This builds a solid foundation for graph interpretation.
2. Improves Analytical Skills: Chapter 13 emphasizes the importance of analyzing data using graphs. By solving these problems, students enhance their analytical and critical thinking skills, which are essential for future math and science courses.
3. Enhances Problem-Solving Ability: The exercises in the NCERT solutions encourage students to solve problems using graphs, which strengthens their ability to handle real-life situations that involve data interpretation.
4. Alignment with School Curriculum: The solutions are aligned with the school curriculum, ensuring that students are well-prepared for their exams, as many questions are directly taken from the NCERT textbook.
5. Practice for Competitive Exams: Since NCERT books are widely recommended for various competitive exams, studying these solutions will give students an edge in preparing for such exams early on.
6. Boosts Confidence: As students practice solving graph-related problems, they gain confidence in their ability to handle questions on this topic during exams.