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Maths For Eco Ii

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Maths For Eco Ii

1. 1. GRAPHS
2. 2. Graphical Technique <ul><li>Most Economic relationships are expressed through graphical presentations. </li></ul><ul><li>Being two dimentional , only two variables can be plotted. </li></ul><ul><li>It is difficult to draw three dimensional figures. </li></ul>
3. 3. Construction of a Graph <ul><li>X-Axis </li></ul><ul><li>Y-Axis </li></ul><ul><li>Cartesian Plane </li></ul><ul><li>Four Quadrants </li></ul><ul><li>Coordinates of a Point </li></ul><ul><li>Abscissa </li></ul><ul><li>Ordinates </li></ul>
4. 4. Cartesian Plane showing the four Quadrants, X Axis and Y Axis <ul><ul><ul><ul><ul><li> +Y Y-Axis </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>II I </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>(-, +) (+, +) </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>-X O +X X-Axis </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>Origin </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>III IV </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li>(-, -) (+, -) </li></ul></ul></ul></ul></ul><ul><ul><ul><ul><ul><li> -Y </li></ul></ul></ul></ul></ul>
5. 5. Locating the position of a point <ul><li>We need minimum two values: </li></ul><ul><li>X- value( ordinate) and </li></ul><ul><li>Y-value(abcissa) </li></ul><ul><li>in order to plot the correct position of a point. </li></ul>
6. 6. Equation represented in a graph <ul><li>1. Linear Equations of two variables </li></ul><ul><li> e.g., 5X + 6Y -11 = 0 </li></ul><ul><li> (form: ax + by + c = 0) </li></ul><ul><li>(Y = a + bX) </li></ul><ul><li>2. Quadratic Equations of two variables </li></ul><ul><li> e.g., Y = X 2 – 6X + 10 </li></ul><ul><li> (form: aX 2 + bX + c = 0) </li></ul><ul><li> </li></ul>
7. 7. Graphing Linear Functions <ul><li>The general form : Y = a + bX </li></ul><ul><li>where a and b are constants. </li></ul><ul><li>Using a specific linear function : </li></ul><ul><li>Y = 3 + 2X </li></ul><ul><li> Prepare the Schedule (Table) </li></ul>
8. 8. Y = 3 + 2x 9 3 7 2 5 1 3 0 Values of Y Values of X
9. 9. <ul><li>We may plot the values graphically thus: </li></ul><ul><li>Y </li></ul><ul><li>10 Y = 3 + 2X </li></ul><ul><li>9 </li></ul><ul><li>8 </li></ul><ul><li>7 </li></ul><ul><li>6 </li></ul><ul><li>5 </li></ul><ul><li>4 </li></ul><ul><li>3 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>o X </li></ul><ul><li>1 2 3 4 5 6 7 </li></ul>
10. 10. Graphing Non-linear function Y = X 2 – 6X + 10 <ul><li>First Prepare the Schedule (Table) </li></ul>5 5 2 4 1 3 2 2 5 1 Values of Y Values of X
11. 11. <ul><li>The values of x and y can be plotted graphically: </li></ul><ul><li>Y </li></ul><ul><li>5 </li></ul><ul><li>4 </li></ul><ul><li>3 Y = X 2 – 6X + 10 </li></ul><ul><li>2 </li></ul><ul><li>1 </li></ul><ul><li>0 X </li></ul><ul><li>1 2 3 4 5 6 </li></ul>
12. 12. Tangent <ul><li>Tangent is a straight line that touches the outside of an arc without intersecting it. </li></ul>
13. 13. Slope <ul><li>Slope : Vertical length = OA </li></ul><ul><li>Horizontal length OB </li></ul><ul><li>A A </li></ul><ul><li> a </li></ul><ul><li> O B </li></ul><ul><li> o B </li></ul><ul><li>If the curve is non-linear, then the slope at a given point ‘a’ ismeasured </li></ul><ul><li>as OA by drawing a tangent AB. OB </li></ul>
14. 14. Slope <ul><li>Slope is also obtained by taking the ratio of change in the value of Y with associated change in the value of X. </li></ul><ul><li>Thus, Slope = Change in Y </li></ul><ul><li>Change in X </li></ul><ul><li>The slope of a curve stands for the rate of change of one variable in relation to a unit change in the associated variables. </li></ul>