Which of the following inequations represents the shaded region?

2 x + y \leq 4

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2 x + y \geq 4

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x + 2 y \leq 4

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x + 2 y \geq 4

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Solution

The correct option is D $2 x + y \leq 4$
The line passes through $(0, 4)$ and $(2, 0)$
Hence equation of the line
$\frac{y}{4} + \frac{x}{2} = 1$
$2 x + y = 4$
Now in the above inequality graph the shading is done towards the origin.
Hence by substituting
$x = 0, y = 0$ we get an inequality which is true.
Hence the possible inequality is $2 x + y < 4$
Now the straight line is dark and not dotted. This indicates that the points on the line are a part of the inequality.
Hence the inequality can be written as
$2 x + y = 4$ or $2 x + y < 4$
$2 x + y \leq 4$ .

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