## NCERT Solutions for Class 8 Maths Chapter 15 Introduction to Graphs Summary

Class 8 NCERT exercise-wise questions and answers as well Example will help students get step-by-step explanations to every question specified in the textbooks. Some of the important topics in NCERT Maths Solutions for Class 8 are graphical representation of data using bar graph chart, pie graph chart, histogram, line graph char and students also learn line graphs and some basic applications of graphs.

## Class 8 Maths Chapter 15 Introduction to Graphs **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 1.30p.m.? How did you arrive at your answer?**

**(e) During which periods did the patients’ temperature show an upward trend?**

**Solution:**

(a) patient’s temperature was 36.5 oC at 1:00 p.m.

(b) the patient’s temperature was 38.5 oC at 12:00.

(c) The patient’s temperature was the same at 1 pm and 2 pm

(d) Temperature at 1:30 p.m. is 36.5 degrees.

The point between 1:00 PM and 2:00 PM is the x-axis equidistant from the two points that point to 1:00 PM. and 2 p.m. So it represents 1:30 p.m. Similarly, a point on the y-axis between 360°C and 370°C represents 36.5°C.

(e) The patient’s temperature showed an upward trend between 9:00 and 11:00. and from 2 p.m. until 3 p.m.

**2. The following line graph shows the yearly sales figures 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 2002and 2006.**

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

**previous year?**

**Solution:**

(a) Sales in 2002 was 4 crores Were 2006 was 8 crores

(b) Sales in 2003 was 7 crores Were 2005 was Rs.10 crores.

(c)

The Sales in 2002 = 4 crore

The Sales in 2006 = 8 crores

Difference = (8 – 4) crore = ₹ 4 crore

(d) In 2005, the difference in sales revenue was the largest with the previous year, which is (10 crores – 6 crores) = Rs. 4 Crores

**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) 3weeks?**

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

**(c) How much did Plant A grow during the 3 ^{rd} week?**

**(d) How much did Plant B grow from the end of the 2nd week to the end of the 3 ^{rd }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.**

**Solution:**

**(a)**

(i)Plant A was 7cm height after 2 weeks And (ii) After 3 weeks it was 9 cm height

**(b)**

(i) The Plant B height was also 7cm after 2 weeks and (ii) After 3 weeks it was 10 cm height

**(c) **The Plant A grew = (9–7) cm = 2cm during 3^{rd} week.

**(d) **Plant B grew from the end of week 2 to the end of week 3 = 10 cm – 7 cm = 3 cm

**(e)** The Plant A grew the highest during 2nd week.

**(f)** The Plant B grew the least during 1st week.

**(g)** Yes. At the end of the second week, plants A and B were the same height, i.e. 7 cm.

**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?**

**Solution:**

(a) On Tuesday, Friday and Sunday, the predicted temperature was the same as the actual temperature.

(b) It was forecast to be 35 degrees.

(c) The lowest actual temperature was 15 oC.

(d) The actual temperature differed the most from Thursday’s predicted temperature.

**5. 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.**

**Solution:**

(a) Consider “years” on the x-axis and “days” on the y-axis. Using the given data, the line graph looks like this:

(b) Consider “years” along the x-axis and “number of males and females” along the y-axis (2 graphs). Using the given data, the line graph looks like this:

**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.**

**(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?**

**Solution:**

(a) The 4 units are = 1hour

(b) The person took 3 ½ hours for the travel.

(c) It was 22 km from the city.

(d) Yes, it is shown in the horizontal part of the diagram. He stayed from 10:00 to 10:30.

(e) He drives fastest between 8:00 and 9:00 AM.

**7. Can there be a time-temperature graph as follows? Justify your answer.**

**Solution:**

(i) This is a time-temperature graph chart. It shows the increase in temperature over time.

(ii) This is a time-temperature chart. It shows a decrease in temperature as time increases.

(iii) Diagram (iii) is not possible because the temperature rises very quickly, which is not possible.

(iv) This is a time-temperature chart. It shows a constant temperature.

## Class 8 Maths Chapter 15 Introduction to Graphs 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)**

**Solution:**

Plot all the points on the graph.

(a) All points A,B, C and D lie on a vertical line.

(b) P,Q, R and S points also make a line .It verifies that these points lie on a line.

(c) Points K, L, M and N. These points do not lie in a straight 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.**

**Solution:**

The Graph for the Line passes through points (2, 3) and (3, 2) is:

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

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

**Solution:**

Here We can observe three figures named such as, OABC, PQRS and LMK.

**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)

**4. 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 co-ordinates of the origin are (0, 0).**

**Solution:**

i) True

ii) False, it will lie on x axis

(iii) True

## Class 8 Maths Chapter 15 Introduction to Graphs **Exercise 15.3**

1. **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 Rs 2500 for a year.**

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

**Solution:**

Mark “number of apples” on the x-axis and “cost” on the y-axis. The graph is

(b) Represent the “time” on the x-axis and “distance” on the y-axis.

(i) The car traveled 20 km

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

(c) Here Represent “Deposit” on the y-axis and “simple interest” on the x-axis.

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

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

(iii) Rs. 3500 should be deposited for interest of Rs. 280

**2. Draw a graph for the following**

**Solution:**

(i) Yes, it is linear graph

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