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| Graphical representation of a Linear Equation
in two variables |
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| The position of a point in a plane is fixed by selecting two axes of reference which are formed by combining two number lines at right angles so that their zeros coincide. |
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| The horizontal number line is called x-axis and the vertical number line is called y-axis. |
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| The point of intersection of the two number lines is called origin. |
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| The two number lines together are called rectangular axes. |
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| The position of a point with respect to the rectangular axes by means of a pair of numbers is called co-ordinates. |
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| The distance OM of point P along x-axis is called x-co-ordinate or abscissa. |
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| The distance ON of point P along y-axis is called ordinate or y-co-ordinate. |
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| If OM=a and ON=b then position of the point P is denoted by (a, b). |
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| Co-ordinates of the origin is (0, 0). |
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| Co-ordinates of any point on the x-axis is (x, 0). |
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| Co-ordinates of any point on the y-axis is (0, y). |
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| The rectangular axes divide the plane into four regions called quadrant. |
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| By convention the quadrants are numbered as I, II, III, IV in the |
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| anticlockwise direction. |
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 Any point in the I quadrant will have both the co-ordinates positive. |
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 In the II quadrant, x-co-ordinates is negative while y-co-ordinate positive. |
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 In the III quadrant, x-co-ordinate as well as y-co-ordinate both are negative. |
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 In the IV quadrant, x-co-ordinate is positive while the y-co-ordinate is negative. |
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 Re-write the given equation expressing one term in terms of the other. |
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| Example: |
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| Find at least 3 sets of values for the variables satisfying the equation. |
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| 2x+y=5 |
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| Express y in terms of x. |
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| y=5-2x |
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| Select three values of x, find corresponding values of y. |
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| x=0, y=5-(2x0)=5 |
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| x=1, y=5-(2x1)=3 |
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| x=-1, y=5-(-2)=7 |
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 Draw the x and y - axes. Choose a suitable scale so as to locate the selected point on the graph. |
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 Plot the selected points. |
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 Draw a straight line joining the points. |
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| Example 1: |
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| Plot the graph of 2x+3y=9. |
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| Suggested answer: |
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| Plot the graph of |
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| 2x+3y=9 |
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| 2x=9-3y |
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| (Expressing one variable in terms of the other) |
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| Put y = 1, |
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| x=3 |
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| Put y = -1, |
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| x=6 |
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| Put y = 7, |
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| x=-6 |
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| Example 2: |
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| Plot the graph of 4x+y=4. |
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| Suggested answer: |
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| Plot the graph of 4x+y=4 |
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| Put y = -4, |
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| x=2 |
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| Put y = 8, |
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| x=-1 |
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| Put y = -8, |
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| x=3 |
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| Example 3: |
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| Plot the graph of 3x-2y=6. |
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| Suggested answer: |
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| Plot the graph of 3x-2y=6 |
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| 3x-2y=6 |
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| 3x=6+2y |
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| Example 4: |
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| Plot the graph of 5x-2y=5. Use the graph to find the area between the line and the axes. |
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| Suggested answer: |
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| Plot the graph of 5x-2y=5 |
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| Area between line and axes = area of D AOB |
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| Example 5: |
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| Plot the graph of x+3y=6. Use the graph to find |
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| a) area between the line and axes |
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| b) value of y when x=-6 |
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| Suggested answer: |
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| x+3y=6 |
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| x=6-3y |
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| y=2, x=6-3y |
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| =6-3(2) |
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| =6-6 |
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| x=0 |
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| y=0, x=6-3y |
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| =6-3(0) |
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| =6-0 |
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| x=6 |
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| y=+3, x=6-3y |
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| =6-3(3) |
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| =6-9 |
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| x=-3 |
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| a) Area between line and axes = area of D AOB |
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| =6 sq.units |
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| b) When x=-6, |
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| x = 6 - 3y , when x = -6, |
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| -6 = 6 - 3y |
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| -6 - 6 = - 3y |
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| -12 = - 3y |
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| \ if x = -6, y = 4 |
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