Example 13. Draw the graphs of the equations
Deter mine the vertices of the triangle formed by the lines representing these equations and the x-axils. Shade the triangular region so formed.
Solution: - Let us take the equation
When,
When,
When,
x | o | 1 | 2 |
y | -4 | 0 | 4 |
We plot the points (0, -4), (1, 0) and (2, 4) on the graph paper and join them. We get a straight line. Now we take the line AB.
4x + y = 121
When x = 2, y = 12 - 4 x 2 = 4
When x = 3, y = 12 - 4 x 3 = 0
When x = 4, y = 12 - 4 x 4 = -4.
x | 2 | 3 | 4 |
y | 4 | 0 | -4 |
We plot the points (2, 4) (3, 0) and (4, -4) on the same graph paper. on joining them we get a line CD which intersect previous line AB. at P (2, 4)
AB intersects the x-axis at (1, 0) and CD intersects the x-axis at (3, 0)
Hence the vertices of the triangle PBD are (2, 4), (1, 0) and (3, 0) . The required region is shaded.
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