NCERT solutions class 8 maths chapter 15 introduction to graphs are given here in a detailed and easy to understand way. Introduction to graphs is a crucial chapter in the NCERT Maths Book for Class 8 and the 8th class CBSE students need to be thorough with all the concepts in this chapter. While solving the exercise questions, students often face some doubts and eventually pile them up. To help the students clear all their doubts instantly, the NCERT class 8 maths solutions for chapter 15 (introduction to graphs) are given here.

The class 8 maths chapter 15 NCERT Solutions contains the introduction to graphs provided here can be easily understood by any class 8 student and can help them clear their doubts. Introduction to graphs is one of the basic concepts in mathematics and students must learn this concept in depth to excel in their higher standard. The class 8 NCERT maths solutions for introduction to graphs are created by the subject experts according to the latest curriculum of CBSE. Also, the for chapter 15 class 8 maths NCERT solutions PDF are provided here which can be downloaded.

### NCERT Solutions Class 8 Maths Chapter 15 Exercises

- NCERT Solutions Class 8 Maths Chapter 15 Introduction to Graphs Exercise 15.1
- NCERT Solutions Class 8 Maths Chapter 15 Introduction to Graphs Exercise 15.2
- NCERT Solutions Class 8 Maths Chapter 15 Introduction to Graphs Exercise 15.3

**Exercise 15.1**

*Q1) The graph given below shows the temperature of a patient observed every hour.*

*(a) What was the temperature of the patient at 2 pm?*

*(b) When was the temperature of the patient \(36.5^{\circ}\)?*

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

*(d) What was the temperature at 12.30 p.m.? How did you come to know it?*

* (e) During which time did the temperature of the patient show a rising trend?*

**Ans.)**

(a) The temperature of the patient was \(36^{\circ}\) C at 2 p.m.

(b) The temperature of the patient was \(36.5^{\circ}\) C at 10 a.m.

The temperature of the patient was the same at 12 p.m. and 1 p.m.

(d) The temperature at 12.30 p.m. is \(37.5^{\circ}\) C. The point between 12 p.m. and 1 p.m., x – axis is equidistant from the two points showing 12 p.m. and 1 p.m. So it represents 12.30 p.m. Similarly the point on y -axis, between \(37^{\circ}\) C and \(38^{\circ}\) C will represent \(37.5^{\circ}\) C.

(e) The temperature of the patient showed a rising trend from 9 a.m. to 11 a.m.

*Q2) The graph given below shows annual sales data for a car manufacturing company.*

*(a) Give the number of sales in the following years:*

*(i) 2012*

*(ii) 2014*

*(b) Give the number of sales in the following years:*

* (i) 2011*

* (ii) 2015*

*What is the difference between the number of sales done in the year 2012 and 2015?*

*(d) In which year was the difference greatest in the numbers of sales compared to its previous year?*

(2011- 5, 2012-8, 2013-7, 2014-11, 2015-9)

**Ans.)**

(a) The numbers of sales:

(i) The sales were Rs. 8 crores, in 2012.

(ii) The sales were Rs. 11 crores, in 2014.

(b) The numbers of sales:

(i) The sales were Rs. 5 crores, in 2011.

(ii) The sales were Rs. 9 crores, in 2015.

I The sales were Rs. 8 crores, in 2012 and the sales were Rs. 9 crores, in 2015.

Therefore, the difference between the sales in 2012 and 2015 = Rs. (9 – 8) crores

= 1 crore

(d) The difference between the sales in 2015 and 2014 = Rs. (11 – 9) crores

= Rs. 2 crores

The difference between the sales in 2014 and 2013 = Rs. (11 – 7) crores

= Rs. 4 crores

The difference between the sales in 2013 and 2012 = Rs. (8 – 7) crores

= Rs. 1 crore

The difference between the sales in 2012 and 2011 = Rs. (8 – 5) crores

= Rs. 3 crores

Therefore, the difference is greatest in the year 2014 as compared to the year 2013.

* *

*Q3) In Botany, for an experiment, two different plants, plant X and plant Y were grown under similar laboratory conditions. The heights of the plants were measured at the end of each week for 4 weeks. The graph given below shows the result of the experiment.*

(X — Start – 0,1 week -1cm, 2 week- 6 cm, 3 week – 9 cm, 4 week- 11cm)

(Y —Start – 0, 1 week -2cm, 2 week- 6 cm, 3 week – 11 cm, 4 week- 13cm)

*Answer the following questions using information given in the graph:*

*(a) How high was Plant X?*

*(i) After 2 weeks *

*(ii) After 3 weeks*

*(b) How high was Plant Y?*

*(i) After 2 weeks *

*(ii) After 3 weeks*

*During the 4 ^{th} week, how much did Plant X grow? *

*(d) During the 3 ^{rd} week and 4^{th} week, how much did Plant Y grow? *

*(e) In which week did Plant X grow maximum?*

* (f) In which week did Plant Y grow least? *

*(g) Specify the week during which both the two plants showed the same height.*

**Ans.)**

(a) The height of Plant X:

(i) The height of Plant Y was 6 cm after 2 weeks

(ii) The height of Plant Y was 9 cm after 3 weeks.

(b) The height of Plant Y:

(i) The height of Plant X was 6 cm after 2 weeks

(ii) The height of Plant X was 11 cm after 3 weeks.

I In 4^{th} week Plant X grew = 11 cm – 9 cm

= 2 cm.

(d) In 3^{rd} week Plant Y grew = 11 cm – 6 cm

= 5 cm

In 4^{th} week Plant Y grew = 13 cm – 11 cm

= 2 cm

(e) Plant X

In 1^{st} week Plant X grew = 1 cm – 0 cm

= 1 cm

In 2^{nd} week Plant X grew = 5 cm – 1 cm

= 4 cm

In 3^{rd} week Plant X grew = 9 cm – 6 cm

= 3 cm

In 4^{th} week Plant X grew = 11 cm – 9 cm

= 2 cm

Therefore, Plant X grew maximum in 2^{nd} week.

(f) Plant Y

In 1^{st} week Plant Y grew = 2 cm – 0 cm

= 2 cm

In 2^{nd} week Plant Y grew = 6 cm – 2 cm

= 4 cm

In 3^{rd} week Plant Y grew = 11 cm – 6 cm

= 5 cm

In 4^{th} week Plant Y grew = 13 cm – 9 cm

= 2 cm

Therefore, Plant Y grew maximum in 3^{rd} week.

(g) Plant X and Y were of the same height at the end of the week 2.

* *

*Q4) The graph given below shows the temperature forecast and the actual temperature for each day of a week. *

*(a) Give the days when the actual temperature was same as the forecast temperature.*

*(b) What was the minimum forecast temperature during the week?*

* What was the maximum actual temperature during the week? *

*(d) On which day was there maximum difference between the actual temperature and the forecast temperature?*

**Ans.)**

(a) The actual temperature was same as the forecast temperature on Tuesday and Thursday.

(b) The minimum forecast temperature was \(15^{\circ}\) C.

I The maximum actual temperature was \(32.5^{\circ}\) C.

(d) The maximum difference between the actual temperature and the forecast temperature was on Wednesday which was \(5^{\circ}\) C.

** **

*Q5) By the use of tables given below, draw linear graphs.*

*(a) In the table below, the number of days when a hill station received snow in different years*

Year |
2003 |
2004 |
2005 |
2006 |

Days |
8 |
10 |
5 |
12 |

* *

*(b) For the different numbers of years, the population (in thousands) of men and women is given below.*

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) Take 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.

(b) 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.

*Q6) A postman cycles from the city to a neighboring village to deliver a package to a grocery dealer. His distance from the city at different times is shown in the following graph.*

* *

*(a) Find out the scale taken for the time axis.*

*(b) Find out the total time that the postman took to travel.*

*(c) Find the distance between the place of grocery dealer to the city.*

*(d) Did the postman stop on the way when he was travelling? Explain.*

*(e) Tell about the period during which he traveled the fastest.*

**Ans.)**

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

(b) The postman travelled during the time period 8 am – 11:30 am.

Therefore, the postman took \(3\frac{1}{2}\) hours to travel

(c) The grocery dealer is 22km far from the city.

(d) Yes, the postman stopped on his way from 10am to 10:30am. This description is indicated by the horizontal part of the graph.

(e) From the graph, it can be observed that during 8am to 9am, the person travelled the maximum distance. Thus, the postman’s ride was fastest between 8am and 9am.

*Q7)Find out whether the time-temperature graph can be represented as follows. Explain with reasons. *

**Ans.) **

(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 the same temperature at different times is possible.

EXERCISE – 15.2

* *

*Q1) Mark the points on a graph sheet, given below are the coordinate of the points.*

* (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) A, B, C and D, these all points lie on a vertical line

(b) All the points P, Q, R and S also lie on a vertical line

These points do not lie on a straight line.

*Q2) Construct a line which passes through (2, 3) and (3, 2). Find out the coordinates of the points at which this line meets the x-axis and y-axis. *

** ****Ans.)**

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

** **

*Q3) Plot the coordinates of the vertices of each of these adjoining figures.*

**Ans.**

Vertices of figure OABC

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

Vertices of figure PQRS P (4, 3), Q (6, 1), R (6, 5) and S (4, 7)

Vertices of figure LMK L (7, 7), M (10, 8) and K (10, 5)

*Q4) Mark True or False in the given Statements and correct the false statements.*

*(i) A line having x coordinate as 0 and y coordinate as a non-zero will lie only on y- axis*

*(ii) When a line is lying on the y-axis, then its y coordinate may be zero and x coordinate may be 5.*

*(iii) Origin have the coordinate as (0,0) *

**Ans.)**

(i) True

(ii) False, it will lie on x – axis.

(iii) True

**Exercise 15.3**

** ***Q1) *

*Draw the graphs for the following tables, with suitable scales on the axes.*

*Cost of the Apple*

* *

Number of Apple |
Cost(in $) |

1 |
5 |

2 |
10 |

3 |
15 |

4 |
20 |

5 |
25 |

* *

*Distance travelled by the car*

Time (in hours) |
Distance (in km) |

6 a.m. |
40 |

7 a.m. |
80 |

8 a.m. |
120 |

9a.m. |
160 |

* *

*How much distance did the car cover during the period 7.30 a.m. to 8 a.m.?**What was the time when the car had covered a distance of 100 km from the car start?**Interest on deposits for a year.*

Deposit (in Rs.) |
Simple Interest (in $) |

1000 |
80 |

2000 |
160 |

3000 |
240 |

4000 |
320 |

5000 |
400 |

* *

*(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?*

**Ans.1)**

(a)

(b) (i) The car covered 20 km distance.

(ii) It was 7.30 am when it covered 100 km distance.

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

(ii) Interest on $2500 is $200 for a year.

(iii) $3500 should be deposited for interest of $280

*Q2.)*

*Draw a graph for the following.*

*(i)*

Side of Square(in cm) |
Perimeter(in cm) |

2 |
8 |

3 |
12 |

3.5 |
14 |

5 |
20 |

6 |
24 |

*Is it a linear graph?*

*(ii)*

Side of Square(in cm) |
Area(in \(cm^{2}\) |

2 |
4 |

3 |
9 |

4 |
16 |

5 |
25 |

6 |
36 |

*Is it a linear graph?*

**Ans 2)**

(i) Yes, it is a linear graph.

(ii) No, it is not a linear graph because the graph does not provide a straight line.

In the introduction to graphs, students are introduced to a wide range of important topics which include the overview of different graph types (bar graph, pie graph, histogram, and line graph), important terminologies such as linear graphs, coordinates, etc. Also, the applications of graphs are given which showcase how important graphs are for real-world uses.

In this chapter, several practice questions are included which is a must-do for all the class 8 students. By practicing, students can easily analyze their level of understanding. Students can always refer to the NCERT class 8 maths solutions for introduction to graphs (chapter 15) here for any doubts.

It is important for the students to be thorough with all the concepts of graphs given in this chapter as graphs are extremely crucial in higher grades. Also, each of the applications discussed in this chapter holds extreme importance in the later grades. Knowing the basics of graphs in a thorough way can help the students to comprehend the higher level concepts easily.

Check out all the NCERT Solutions For Class 8 Maths here in detail for all the individual chapters. These NCERT solutions not only help the students to clear all their doubts instantly but also help them to learn all the maths concepts in a more effective and in-depth way.