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Linear Graphs Linear Graphs Linear Graphs Linear Graphs

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Page 1: Linear Graphs Linear Graphs Linear Graphs Linear Graphs

Linear Graphs

Linear Graphs Linear Graphs Linear Graphs

Page 2: Linear Graphs Linear Graphs Linear Graphs Linear Graphs

CARTESIAN SYSTEMAXISORIGIN

AXIS DIRECTIONS

LOCATING POINTS IN THE CARTESIAN PLANE

Example 1

TOPICS

APPLICATIONS OF LINEAR GRAPH

Example 2

Theory

Exercise

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Cartesian Coordinate System consists of two axes, X and Y, which intersect each other at a point called `origin`, and is used to define the position of any point by using ordered pairs.

We call the plane, the Cartesian plane, or the coordinate plane, or the xy-plane.

CARTESIAN SYSTEM

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X′X is called the horizontal axis and write the numbers on it both negative and positive on either side of zero.

Y′Y is called the vertical axis and write the numbers on it both negative and positive on either side of zero.

AXIS

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Combine both the lines (Horizontal and Vertical axes)in such a way that the two lines cross each other at their zeroes is called as origins.

Origin O(0, 0)

ORIGIN

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+ve - Axis Directions

The positive numbers lie on the directions OX and OY, OX and OY are called the positive directions of the x - axis and the y - axis, respectively.

ve - Axis DirectionsThe negative numbers lie on the directions OX’ and OY’, OX’ and OY’ are called the negative directions of the x - axis and the y - axis, respectively.

AXIS DIRECTIONS

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LOCATING POINTS IN THE CARTESIAN PLANE

(5, 0)

(5, 0)

(4, 3)

(4, 3)

(7, 9)(7, 9)(0, 8)

(0, 8)

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The equation of a straight-line graph contains:

Independent variable (x)

Dependent variable (y)

The relation between independent and dependent variables can be shown through a graph.

Example

2x – y – 1 = 0

APPLICATIONS OF LINEAR GRAPHTheory

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2x – y – 1 = 0

APPLICATIONS OF LINEAR GRAPH

xy112359

(1, 1)

(2, 3)

(5, 9)

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APPLICATIONS OF LINEAR GRAPHExample 1

532

9C F F

The relationship between Celsius and Fahrenheit temperatures is given by formula:

Draw the linear graph for this relationship.

°C 0 5 10 15 20

°F 32 41 50 59 68

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APPLICATIONS OF LINEAR GRAPHExample 2

A cab company charges a Rs 15 boarding rate in addition to its meter which is Rs 8 for every kilometer. Draw the linear graph for this statement.

Distance 1 2 3 4 5Charges 23 31 39 47 55

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EXERCISEA cab company charges a $5 boarding rate in addition to its meter which is $3 for every mile.

Draw the graph for the following relationship.

2 3 0x y

A bank gives 10% Simple Interest (S.I.) on deposits of Rs 1000 per year. Draw a graph to illustrate the relation between interest earn for five continuous years.