INTRODUCTION TO GRAPHSChapter 2 , Unit 5 Maths - Class VIII

Module Objectives

• When should you use graphs?

• Understanding the rectangular coordinate system• Drawing graphs of linear curves in a coordinate

system• Constructing equations of a straight line by looking

at a graph

Topics• 2.5.1 – Introduction• 2.5.2 – Bar Graphs • 2.5.3 – Pie Charts• 2.5.4 – Coordinate System• Example• 2.5.5 – Linear Graphs• Points to Remember• Exercises• Glossary• Solutions

2.5.1 Introduction

• Graphs are visual representations of data collected. • Data can also be presented in the form of a table; however a

graphical presentation is easier to understand.

• Click here to find out 'what is a graph?'

2.5.2 Bar Graphs• A bar graph is used to show comparison among categories. • The categories being compared do not need to affect one another• It may consist of two or more parallel vertical (or horizontal)

bars/rectangles.• In the below table, which data is easier to understand?

Bar Graph Raw Data

A firm makes a profit of ` 36 lakhs during 2006, ` 48 lakhs during 2007, ` 70 lakhs during 2008, ` 85 lakhs during 2009 and ` 75 lakhs during 2010.

2.5.3 Pie Charts

• A pie chart or pie-graph is used to compare parts of a whole. • The circle represents the whole.• This kind of graph is needed to show percentages effectively.• Example

Rahmi’s total income: Rs. 36,000Total Angle at the center of the pie chart is 360°Sector Angle = Ratio of Expenditure to his income * 360°

Rahims Expenditure Rs. Sector Angle

House Rent 6,000 60°

Food 6,000 60°

Children's Education 3,600 36°

Miscellaneous 6,000 60°

Parental Care 6,000 60°

Savings 8,400 84°

2.5.4 Coordinate System• A very useful method of representing data is the use of Cartesian

graphs. These are also called as Coordinate graphs, as its based on the Coordinate system.

• A coordinate system is used to represent points in a plane.• Location of a point

Example - The teacher put a dot on the black-board. She asked the students how they would describe its location.

Can any one of these statements help fix the position of the dot? No! There is a need to measure the relative position of a point from some reference. This is the main purpose of a coordinate system.

• How does a simple Coordinate system look?

• It consists of 2 perpendicular lines in a plane – x-axis (horizontal) and y-axis (vertical). The point of intersection is the origin (0,0)

• Values on x-axis are positive to the right of origin, and negative to the left. Values on y-axis are positive to the top of origin, and negative to the bottom.

• A point is represented as (X,Y) – X is Abscissa, Y is Ordinate• Recap of Coordinate System

The given graph describes the distances of a car from a city P at different times when it is travelling from City P to City Q, which are 350 km apart. Study the graph and answer the following:

(i) When did the car begin its journey?

(ii) How far did the car go in the first hour?

(iii) How far did the car go during (a) the 2nd hour? (b) the 3rd hour?

(iv) Did the car stop for some duration at any place? Justify your answer.

(v) When did the car reach City Q?

Example

(i) When did the car begin its journey?The car started from City P at 8 a.m

(ii) How far did the car go in the first hour?The car travelled 50 km during the first hour. [This can be seen as follows. At 8 a.m. it just started from City P. At 9 a.m. it was at the 50th km (seen from graph). Hence during the one-hour time between 8 a.m. and 9 a.m. the car travelled 50 km]

(iii) How far did the car go during (a) the 2nd hour? (b) the 3rd hour?The distance covered by the car during(a) 2nd hour (i.e., from 9 am to 10 am) is 100 km [150 – 50](b) 3rd hour (i.e., from 10 am to 11 am) is 50 km [200 – 150]

(iv) Did the car stop for some duration at any place? Justify your answer.We find that the car was 200 km away from city P when the time was 11 a.m. and also at 12 noon. This shows that the car did not travel during the interval 11 a.m. to 12 noon.

(v) When did the car reach City Q?The car reached City Q at 2 p.m.

-5

0

5

10

15

-3 -2 -1 0 1 2 3 4

Y A

xis

X Axis

Y = 3 X + 5

2.5.5 Linear Graphs

• Line graph consists of bits of line segments joined consecutively. • Sometimes the graph may be a whole unbroken line. Such a

graph is called a Linear graph. • Example : ‘y = 3x + 5’

x 0 1 2 3 -1 -2

y 5 8 11 14 2 -1

Points to Remember

• Graphical presentation of data is easier to understand.• A bar graph is used to show comparison among categories.• A pie graph is used to compare parts of a whole.• A linear graph displays data that changes continuously over

periods of time.• Rectangular coordinate system is a plane which can be

divided into 4 parts called Quadrants• For fixing a point on the graph sheet we need, x-coordinate

and y-coordinate.

Exercises

1. Fill in the Blanks:a) The y-coordinate of a point on the x-axis is b) If a point (x,y) lies above horizontal axis, then y is always c) The point of intersection of ‘x = y’ and ‘x = -y’ is d) The line ‘y = 4x + 5’ intersects y-axis at the point

2. Match the following:a) On the x-axis i) x-coordinate is negativeb) In the second quadrant ii) cuts the y-axis at (0,4)c) The line ‘y = 3x + 4’ iii) coordinates of a point are of

the form (a,0)

3. Choose the correct option:a) The point (4,0) lies on the line

A. y – x = 0 B. y = 0 C. x = 0 D. y + x = 0 b) The point (-5,4) lies in quadrant

A. First B. Second C. Third D. Fourthc) The coordinates of a point P in a system X’OX Y’OY are (5,8).

The coordinates of the same point in system Y’OY X’OX are

A. (–8,5) B. (8,5) C. (8, –5) D. (–8, –5)

4. True or False?a) The equation of the x-axis is ‘x = 0’.b) The line y = 8 is perpendicular to x-axis.c) The graph of ‘y = x2 ’ is a straight line.d) The line ‘y = 3x + 4’ does not intersect x-axis.

Glossary

• Graph – a visual representation of numerical data• Bar graph – data is represented by rectangular bars• Pie graph – data is represented by sectors of a circle• x-axis – horizontal line in a rectangular coordinate system • y-axis – vertical line in a rectangular coordinate system• Quadrant – four parts of the rectangular coordinate system• Abscissa – the x-coordinate of a point• Ordinate – the y-coordinate of a point

Solutions1. Fill in the Blanks:

a) zero b) negative c) (0,0) d) (0,5)

2. Match the following: a) iii)b) i) c) ii)

3. Choose the correct option:a) B b) B c) C

• True or False?a) False b) False c) False d) False