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Encapsulate
math
INTRODuCTION TO gRAPHS

Coordinate Axes and Number line
Cartesian Plane
Number line represents numbers at equal gaps from a neutral
Y point called origin.
Origin
4
y-axis
Second First P Q
3
Quadrant Quadrant
(–, +) (+, +) –4 –3 –2 –1 0 1 2 3 4
2
(Negative Numbers) (Positive Numbers)
Origin x-axis
1
Coordinates of a point
O
X –4 –3 –2 –1 1 2 3 4 X
–1
• the distance Y
–2 4
Third Fourth from y-axis Tells us how many units
Quadrant Quadrant to move towards
–3 (OM) is called the right.
(–, –) (+, –) 3
x-coordinate or P(x, y) or (3, 2)
–4 2
Y abscissa of P Tells us how many
1 Ordinate y units to move
Here X′OX and YOY′ taken together are • the distance M upward.
called coordinate axes. The plane divided from x-axis X′ –4 –3 –2 –1 O 1 2 3 4 X
into four quadrants by two coordinate (PM)is called –1 Abscissa
x
axes is called the Cartesian plane.
y-coordinate or –2
ordinate of P –3
–4
Y′

Some Applications

Linear graph: If the graph obtained is a straight line, Line graph: A line graph displays data that changes
then it is called a linear graph. For example, continuously over the periods of time. For example,
Sum (in `) 100 200 300 500 Time 6 a.m. 10 a.m. 2 p.m. 6 p.m. 10 p.m.
Annual S.I. (in `) 10 20 30 50 Temperature
(in °C) 37 40 38 36 35
Y
Scale: On x-axis, 1 unit = `100
80 Y Scale: On x-axis, 1 unit = 4 h
On y-axis, 1 unit = `10
On y-axis, 1 unit = 2° C
70 40
60 (500, 50) 38
Annual Simple Interest (in `) 40 (200, 20) Temperature (in °C) 34
50
36

30
(300, 30)
32
20
30
10
(100, 10)
0 X
X 6 a.m. 10 a.m. 2 p.m. 6 p.m. 10 p.m.
O(0, 0) 100 200 300 400 500 600 700 800 Time
Deposit (in `)
Mathematics-8 330