NCERT Solutions for Class 8 Maths Chapter 13 Introduction to Graphs

NCERT
SOLUTIONS
CLASS - 8TH

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

Class : 8th
Subject : Maths
Chapter : 15
Chapter Name : Introduction to Graphs

Exercise 15.1

Q1 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 patients’ temperature showed an upward trend?

Answer. (a) At 1 p.m., the patient's temperature was 38.5° C.
(b) The patient's temperature was 38.5° C at 12 noon.
(c) The patient's temperature was same at 1 p.m. and 2 p.m.
(d) The graph between the times 1 p.m. and 2 p.m. is parallel to the x-axis. The temperature at 1 p.m. and
2 p.m. is 36.5° C. So, the temperature at 1:30 p.m. is 36.5° C

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Book : Mathematics Ncert Solutions | Chapter-15 Maths
(e) During the following periods, the patient's temperature showed an upward trend. 9 a.m. to 10 a.m., 10
a.m. to 11 a.m., 2 p.m. to 3 p.m.

Page : 236 , Block name : Exercise 15.1

Q2 The following line graph shows the yearly sales gures 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

Answer. (a) (i) 2002, the sales were Rs 4 crores.
(ii) In 2006, the sales were Rs 8 crores.
(b) (i) In 2003, the sales were Rs 7 crores.
(ii) In 2005 the sales were Rs 10 crores.
(c) (i) In 2002 the sales were Rs 4 crores and in 2006, the sales were Rs 8 crores.
Difference between the sales in 2002 and 2006 = Rs (8 -4) crores =Rs 4 crores
(d) Difference between the sales of the year 2006 and 2005 = Rs (10-8) crores =Rs 2 crores
Difference between the sales of the year 2005 and 2004= Rs (10 - 6) crores = Rs 4 crores
Difference between the sales of the year 2004 and 2003= Rs (7-6) crore = Rs 1 crore
Difference between the sales of the year 2003 and 2002 =Rs (7 -4) crores =Rs 3 crores
Hence, the difference was the maximum in the year 2005 as compared to its previous year

Page : 237 , Block name : Exercise 15.1

Q3 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

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

(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

Answer. (i) After 2 weeks, the height of plant A was 7 cm.
(ii) After 3 weeks, the height of plant A was 9 cm.
(b) (i) After 2 weeks, the height of plant B was 7 cm.
(ii) After 3 weeks the height of plant B was 10 cm.
(c) Growth of plant A during 3rd week = 9 cm -7 cm = 2 cm
(d) Growth of plant B from the end of the 2nd week to the end of the 3rd week = 10 cm -7 cm =3 cm
(e) Growth of plant A during 1st week = 2 cm -0 cm = 2 cm
Growth of plant A during 2nd week = 7 cm - 2 cm = 5 cm
Growth of plant A during 3d week =9 cm -7 cm= 2 cm
Therefore, plant A grew the most, i.e. 5 cm, during the 2nd week.
(f) Growth Of plant B during ISt week = 1 cm -0 cm =1 cm
Growth of plant 3 during 2nd week = 7 cm -1 cm = 6 cm
Growth Of plant 3 during 38 week = 10 cm -7 cm = 3 cm
Therefore, plant B grew the least, i.e. 1 cm, during the 1st week.
(g) At the end of the 2nd week, the heights of both plants were same.

Page : 237 , Block name : Exercise 15.1

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Book : Mathematics Ncert Solutions | Chapter-15 Maths
Q4 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?

Answer. (a) The forecast temperature was same as the actual temperature on Tuesday,
Friday, and Sunday.
(b) The maximum forecast temperature during the week was 35° C.
(c) The minimum actual temperature during the week was 35° C.
(d) The actual temperature differs the most from the forecast temperature on
Thursday.

Page : 238 , Block name : Exercise 15.1

Q5 Use the tables below to draw linear graphs.
(a) The number of days a hill side city received snow in different years.

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

Answer. (a) By taking the years on x-axis and the number of days on y-axis and taking scale
as 1 unit = 2 days on y-axis and 2 unit = 1 year on x axis, the linear graph of the
given information can be drawn as follows.

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

(b) dy taking the years on x-axis and population on y-axis and scale as 1 unit 0.5 thousand on y-axis and
2 unit = 1 year on x-axis, the linear graph of the given information can be drawn as follows.

Page : 238 , Block name : Exercise 15.1

Q6 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.
(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?

Answer. (a) Scale taken for the time axis is 4 units = 1 hour
(b) The person travelled during the time 8 a.m. -11:30 a.m. Therefore, the person took 3 hours to
1

2

travel.
(c) The merchant is 22 km far from the town.
(d) Yes, the person stopped on his way from 10 a.m. to 10: 30 a.m. This is indicated by the horizontal part
of the graph.
(e) From the graph, it can be observed that during 8 a.m. to 9 a.m., the person travelled the maximum
distance. Thus, the person's ride was the fastest between 8 a.m. and 9 a.m.

Page : 239 , Block name : Exercise 15.1

Q7 Can there be a time-temperature graph as follows? Justify your answer

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

Answer. (i) This can be a time-temperature graph, as the temperature can increase with the
increase in time.
(ii) This can be a time-temperature graph, as the temperature can decrease with the decrease in time.
(iii) This cannot be a time-temperature graph since different temperatures at the same time are not
possible.
(iv) This can be a time-temperature graph, as same temperature at different times
is possible.

Page : 239 , Block name : Exercise 15.1

Exercise 15.2

Q1 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)

Answer. (a) We can plot the given points and join the consecutive points on a graph paper as follows.

From the graph, it can be observed that the points A, 3, C, and D lie on the same line.
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Book : Mathematics Ncert Solutions | Chapter-15 Maths
(b) We can plot the given points and join the consecutive points on a graph paper as follows.

Hence, points p, Q, R, and S lie on the same line.
(c) We can plot the given points and join the consecutive points on a graph paper as follows.

Hence, points K, L, M, and N are not lying on the same line.

Page : 243 , Block name : Exercise 15.2

Q2 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.

From the graph, it Can be observed that the line joining the points (2, 3) and (3, 2) meets the x-axis at the
point (5, 0) and the y-axis at the point (0, 5).

Page : 243 , Block name : Exercise 15.2

Q3 Write the coordinates of the vertices of each of these adjoining gures.

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

Answer. The coordinates of the vertices in the given gure 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)

Page : 243 , Block name : Exercise 15.2

Q4 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)

Answer. (i) True
(ii) False
The point whose y-coordinate is zero and X-coordinate is 5 will lie on x-axis.
(iii) True

Page : 243 , Block name : Exercise 15.2

Exercise 15.3

Q1 . Draw the graphs for the following tables of values, with suitable scales on the axes.
(a) Cost of apples

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

(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 nd the interest on 2500 for a year.
(iii) To get an interest of 280 per year, how much money should be deposited?

Answer. (a) Taking a suitable scale (for x-axis, 1 unit =1 apple and for y-axis, 1 unit =Rs 5), we can mark
the number of apples on x-axis and the cost Of apples on y-axis. A graph Of the given data is as follows.

(b) Taking a suitable scale (for x-axis, 2 units = 1 hour and for y axis, 2 units =40 km), we can represent
the time on x-axis and the distance covered by the car on y- axis. A graph of the given data is as follows.

(i) During the period 7:30 a.m. to 8 a.m., the car covered a distance of 20 km.
(ii) The car covered a distance of 100 km at 7:30 a.m. since its start.

(c) Taking a suitable scale,
For x-axis, 1 unit Rs 1000 and for y-axis, 1 unit Rs 80
We can represent the deposit on x-axis and the interest earned on that deposit on y- axis. A graph Of the
given data is obtained as follows.

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Book : Mathematics Ncert Solutions | Chapter-15 Maths

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.

Page : 248 , Block name : Exercise 15.3

Q2 Draw a graph for the following.
(i) Is it a linear graph?

(ii)
Is it a linear graph?

Answer. (i) Choosing a suitable scale,
For x-axis, 1 unit = 1 cm and for y-axis, 1 unit = 4cm2

We can represent the side of a square on x-axis and the perimeter of that square on y-axis. A graph Of
the given data is drawn as follows.

It is a linear graph
(ii) Choosing a suitable scale, For x-axis, 1 unit 1 cm and for y-axis, 1 unit =4cm
2

We can represent the side Of a square on the x-axis and the area Of that square on
y-axis. A graph Of the given data is as follows.

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Book : Mathematics Ncert Solutions | Chapter-15 Maths
It is not a linear graph

Page : 248 , Block name : Exercise 15.3

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