NCERT Solutions Class 8 Maths Chapter 13 Introduction to Graphs

• Exercise 13.1: This exercise introduces the Cartesian Plane. The objective is to understand the basics of the Cartesian plane and how to plot points. The Key Concepts are the cartesian coordinate system, identifying and plotting points using (x,y) coordinates, and understanding the x-axis and y-axis.

• Exercise 13.2: This exercise explains how to draw and interpret line graphs. Key Concepts are plotting data points on a graph, connecting points to form a line graph, and interpreting trends and patterns from line graphs.

Access NCERT Solutions for Class 8 Maths Chapter 13 – Introduction to Graphs

Exercise 13.1

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 1.30 p.m? How did you arrive at your answer? 

(e) During which periods did the patient’s temperature show an upward trend?

Graph ( temperature vs time), Image Credits-NCERT

Ans: (a) The patient's temperature was $36.5{}^\circ C$at $1$ p.m.

(b) At $12$ p.m., the patient's temperature was $38.5{}^\circ C$.

(c) At 1 p.m. and 2 p.m., the patient's temperature was the same.

(d) The graph between $1$ and $2$ p.m. is parallel to the x-axis. At $1$ p.m. and $2$ p.m., the temperature is $36.5{}^\circ C$. So, $1:30$p.m., the temperature is $36.5{}^\circ C$.

(e) The patient's temperature showed an upward trend in the following periods.

$9$ a.m. to $10$ a.m., $10$ a.m. to $11$ a.m., $2$ p.m. to $3$ p.m.

2: 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?

Graph Sales ( in Rs crores ) Vs Years, Image Credits-NCERT

Ans: (a) 

(i)The sales in $2002$ were Rs $4$crores.

(ii)The sales in $2006$ were Rs $8$crores.

(b)

(i)The sales in $2003$ were Rs $7$crores.

(ii)The sales in $2005$ were Rs $10$crores.

(c)Difference between the sales in $2002$ and $2006$

= Rs ($8$ − $4$) crores

 = Rs $4$ crores 

(d)Difference between the sales in $2006$ and $2005$

= Rs ($10$ − $8$) crores

 = Rs $2$ crores 

Difference between the sales in $2005$ and $2004$

= Rs ($10$ − $6$) crores

 = Rs $4$ crores 

Difference between the sales in $2004$ and $2003$

= Rs ($7$ − $6$) crores

 = Rs $1$ crores 

Difference between the sales in $2003$ and $2002$

= Rs ($7$ − $4$) crores

 = Rs $3$ crores 

As a result, the difference was greatest in $2005$ as compared to the prior year, $2004$.

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) $3$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.

Graph Height ( in cm ) Vs Weeks, Image Credits-NCERT

Ans: (a) (i)Plant A had grown to a height of $7$ cm after two weeks.

(ii) Plant A grew to a height of $9$ cm after three weeks.

(b) Plant B grew to a height of $7$ cm after two weeks.

(ii) Plant B grew to a height of $10$ cm after three weeks.

(c)Plant A's growth during the third week = $9-7$ 

= $2$cm

(d)Plant B's growth from the end of the second to the end of the third week 

=$10-7$ 

= $3$cm

(e) Plant A's growth over the first week = $2-0$ 

= $2$cm

Plant A's growth over the second week = $7-2$

= $5$cm

Plant A's growth during the third week = $9-7$

= $2$cm

As a result, during the second week, plant A grew the most, gaining $5$cm.

(f)Plant B's growth over the first week = $1-0$ 

= $1$cm

Plant B's growth over the second week = $7-1$

= $6$cm

Plant B's growth during the third week = $10-7$

= $3$cm

As a result, during the first week, plant B grew the least i.e. $1$cm.

(g)The heights of both plants were the same at the conclusion of the second week.

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? 

Graph Temperature  Vs Days, Image Credits-NCERT

Ans: (a) On Tuesday, Friday, and Sunday, the forecast temperature matched the actual temperature.

(b)The maximum forecast temperature during the week was $35{}^\circ C$. 

(c) The minimum actual temperature during the week was $15{}^\circ C$.

(d)On Thursday, the actual temperature differs the most from the forecast 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.

Ans:(a)

The linear graph of the given information can be constructed using the years on the x-axis and the number of days on the y-axis, with scales of $1$ unit = $2$ days on the y-axis and $2$unit = $1$ year on the x-axis. 

Graph Days  Vs Years

(b)

The linear graph of the given information may be constructed by plotting the years on the x-axis and the population on the y-axis, with scales of $1$ unit = $0.5$ thousand on the y-axis and $2$ unit = $1$ year on the x-axis.

Graph Population(in thousand) Vs Years

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. 

Graph Distance (in km)  Vs Time, Image Credits-NCERT

(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? 

Ans:

(a) Scale taken for the time axis is $4$ units = $1$ hour
(b) The person travelled between the hours of $8$ a.m. and $11:30$ a.m. As a result, the guy had to travel for $3\frac{1}{2}$  hours. 

(c) The merchant is $22$ kilometres away from town. 

(d) Yes, from $10$a.m. to $10:30$ a.m., the person came to a halt. 

The graph's horizontal portion indicates this. 

(e) The graph shows that the person travelled the greatest distance between the hours of $8$ a.m. and $9$ a.m. 

As a result, the person's ride was the quickest between $8$ and $9$a.m. 

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

Graph Temperature Vs Time, Image Credits-NCERT

Ans:(i)This might be a time−temperature graph, as the temperature rises with the passage of time. 

(ii) This might be a time−temperature graph, as the temperature can drop as time passes. 

(iii) This isn't a time−temperature graph because it's impossible to have various temperatures at the same time. 

(iv) This can be a time−temperature graph, as the same temperature can be found at different times. 

Exercise 13.2

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 its 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? 

Ans: (a)  We may mark the quantity of apples on the x-axis and the cost of apples on the y-axis using a suitable scale ($1$ unit = $1$ apple on the x-axis and $1$unit = Rs $5$ on the y-axis).

The following is a graph of the given data.

Graph Cost(Rs) Vs Number of Apples

(b) Using a suitable scale ($2$ units = $1$ hour on the x-axis and $2$ units = $40$ kilometres on the y-axis), we can display the time on the x-axis and the distance travelled by the car on the y-axis.

The following is a graph of the given data.

Graph Distance (km) Vs Time (hours)

(i) The car covered a distance of $20$ kilometres between $7:30$ a.m. and $8$ a.m.

(ii) At $7:30$ a.m., the car had travelled $100$ kilometres since it began.

c) Selecting an appropriate scale

$1$ unit equals Rs $1000$ on the x-axis and Rs $80$ on the y-axis.

On the x-axis, we can represent the deposit, and on the y-axis, we can indicate the interest earned on that account.

The following is a graph of the given data. 

Graph Simple Interest Vs Deposit (Rs)

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. 

2:Draw a graph for the following. 

(i) 

Is it a linear graph? 

Is it a linear graph? 

Ans:(i)Selecting an appropriate scale

$1$ unit equals $1$ cm on the x-axis and $4$ cm on the y-axis.

On the x-axis, we may represent a square's side, and on the y-axis, we can represent the square's perimeter.

The following is a graph of the given data.

Graph Perimeter (cm) Vs Side of Square (cm)

It is a linear graph.

(ii)Selecting an appropriate scale

$1$ unit = $1$ cm on the x-axis and $4$ cm2 on the y-axis

On the x-axis, we may indicate the side of a square, and on the y-axis, we can represent the area of that square.

Graph Area (square meter) Vs Side of Square (cm)

The following is a graph of the given data. It is not a linear graph.

Overview of Deleted Syllabus for CBSE Class 8 Maths Introduction to Graphs

Class 8 Maths Chapter 13: Exercises Breakdown

Conclusion

Introduction To Graphs for Class 8 is an essential part of the Maths curriculum. It equips students with essential skills for plotting and interpreting various types of graphs. By mastering the Cartesian plane, understanding different graph types, and applying these concepts to real-world data, students enhance their ability to visualize and analyze information effectively. The chapter's emphasis on practical applications helps students appreciate the relevance of graphs in everyday life, from tracking changes over time to comparing different sets of data. This chapter is significant in exams, with an average of 3-4 questions being asked in previous years.

Other Study Material for CBSE Class 8 Maths Chapter 13

Chapter-Specific NCERT Solutions for Class 8 Maths

Given below are the chapter-wise NCERT Solutions for Class 8 Maths. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.