# NCERT Solutions for Class 8 Maths Maths - NCERT Solution Chapter 15

## Introduction to Graphs Class 8

### Exercise 15.1 : Solutions of Questions on Page Number : 236

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 patient's temperature show an upward trend?

(a) At 1 p.m., the patient's temperature was 36.5°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.

(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.

Q2 :

The following line graph shows the yearly sales figure 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?

(a)

(i) In 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 2004.

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.

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

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

(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.

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?

Q5 :

Use the tables below to draw linear graphs.

(a) The number of days a hill side city received snow in different years.

 Year 2003 2004 2005 2006 Days 8 10 5 12

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

 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

Q6 :

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?

Q7 :

Can there be a time temperature graph as follows? Justify you're answer:

 (i) (ii) (iii) (iv)

### Exercise 15.2 : Solutions of Questions on Page Number : 243

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)

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.

Q3 :

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

Q4 :

State whether True or False. Correct those 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).

### Exercise 15.3 : Solutions of Questions on Page Number : 247

Q1 :

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

(a) Cost of apples

 Number of apples 1 2 3 4 5 Cost (in Rs) 5 10 15 20 25

(b) Distance travelled by a car

 Time (in hours) 6 a.m. 7 a.m. 8 a.m. 9 a.m. Distance (in km) 40 80 120 160

(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 its start?

(c) Interest on deposits for a year:

Q2 :

Draw a graph for the following.

(i)

 Side of square (in cm) 2 3 3.5 5 6 Perimeter (in cm) 8 12 14 20 24

Is it a linear graph?

(ii)

 Side of square (in cm) 2 3 4 5 6 Area (in cm2) 4 9 16 25 36

Is it a linear graph?