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Question
Sketch the graph of inequation x ≥ 5y in xoy co-ordinate system
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Solution
Given inequation: x ≥ 5y
i.e., x − 5y ≥ 0
∴ Corresponding equation is x − 5y = 0
It is a line passing through origin O (0, 0).
To find another point on the line, we can take any value of x.
Substituting x = 5 in x − 5y = 0, we get
5 − 5y = 0
∴ 5 = 5y
∴ y = 1
∴ Another point on the line is A(5, 1).
∴ The line passes through O(0, 0) and A(5, 1).
Choose a point (1, 0) not lying on the line.
∴ Substituting x = 1, y = 0 in x ≥ 5y, we get 1 ≥ 0
∴ (1, 0) satisfies the given inequality.
∴ The required region is on the side containing the point (1, 0).
The shaded portion represents the graphical solution.
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