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Question
Draw the graph of the following equations :
3x + 2y + 6 = 0
3x + 8y - 12 = 0
Also, determine the co-ordinates of the vertices of the triangle formed by these lines and x-axis.
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Solution
3x + 2y + 6 = 0 ...(1)
3x + 8y - 12 = 0 ...(2)
3x + 2y = -6
⇒ 3x = -6 - 2y
Corresponding values of x and y can be tabulated as :
| x | -2 | 0 | -2.66 |
| y | 0 | -3 | 1 |
Plotting points (-2, 0), (0, 3), (-2.66, 1) and joining them, we get a line l1 which is the graph of equation (1).
3x + 8y - 12 = 0
⇒ 3x = 12 - 8y
Corresponding values of x and y can be tabulated as :
| x | 4 | -4 | 0 |
| y | 0 | 3 | 1.5 |
Plotting points (4, 0), (-4, 3), (0, 1.5) and joining them, we get a line l2 which is the graph of equation (2).
It can be seen that the two lines l1 and l2 and the x-axis from a triangle ABC.
The coordinates of the vertices of ΔABC are A(-4, 3), B(-2, 0) and C(4, 0).
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