1. Linear Graphs Linear Graphs Linear Graphs Linear Graphs

2. CARTESIAN SYSTEM AXIS ORIGIN AXIS DIRECTIONS LOCATING POINTS IN THE CARTESIAN PLANE Example 1 TOPICS APPLICATIONS OF LINEAR GRAPH Example 2 Theory Exercise

3. 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

4. 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

5. 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

6. +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 Directions The 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

7. LOCATING POINTS IN THE CARTESIAN PLANE (5, 0) (5, 0) (4, 3) (4, 3) (7, 9) (7, 9) (0, 8) (0, 8)

8. 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 GRAPH Theory

9. 2x – y – 1 = 0 APPLICATIONS OF LINEAR GRAPH (1, 1) (2, 3) (5, 9)

10. Example 1 The relationship between Celsius and Fahrenheit temperatures is given by formula: Draw the linear graph for this relationship. °C05101520 °F3241505968

11. APPLICATIONS OF LINEAR GRAPH Example 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 12345 Charges 2331394755

12. A 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. 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.