The shaded region in the given figure is a graph of ..... - Vidyadip

MCQ

The shaded region in the given figure is a graph of $.....$

A
$4 x-2 y \leq 3$
✓
$4 x-2 y \leq-3$
C
$2 x-4 y \geq 3$
D
$2 x-4 y \leq-3$

✓

Answer

Correct option: B.

$4 x-2 y \leq-3$

b
The given line intersects $\mathrm{X}$ - axis at $\left(-\frac{3}{4}, 0\right)$ and $\mathrm{Y}$ - axis at $\left(0, \frac{3}{2}\right)$

$\therefore$ Equation of the line $\frac{x}{-\frac{3}{4}}+\frac{y}{\frac{3}{2}}=1$

$\therefore-4 x+2 y=3$

$\therefore 4 x-2 y=-3$

Taking $x=y=0 \Rightarrow 0-0 \leq-3$ which is not true.

$\therefore 4 x-2 y \leq-3$ is a half plane not containing $(0,0).$

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