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Question
Sketch the graph of the following inequation in XOY co-ordinate system:
|x + 5| ≤ y
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Solution
|x + 5| ≤ y
∴ - y ≤ x + 5 ≤ y
∴ - y ≤ x + 5 and x + 5 ≤ y
∴ x + y ≥ - 5 and x - y ≤ - 5
First we draw the lines AB and AC whose equations are x + y = - 5 and x - y = - 5 respectively.
| Line | Equation | Points on the X-axis | Points on the Y-axis | Sign | region |
| AB | x + y = - 5 | A(- 5, 0) | B(0, -5) | ≥ | origin side of line AB |
| AC | x - y = - 5 | A(-5, 0) | C(0, 5) | ≤ | non-origin side of line AC |
The graph of |x + 5| ≤ y is as below:
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