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(B) The given line passes through the points $B\left(-\frac{3}{4}, 0\right)$ and $A\left(0, \frac{3}{2}\right)$.The equation of the line in intercept

Vedclass · Accepted Answer

$4 x-2 y \leq-3$

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(B) The given line passes through the points $B\left(-\frac{3}{4}, 0\right)$ and $A\left(0, \frac{3}{2}\right)$.The equation of the line in intercept form is $\frac{x}{a} + \frac{y}{b} = 1$,where $a = -\frac{3}{4}$ and $b = \frac{3}{2}$.Substituting the values,we get $\frac{x}{-\frac{3}{4}} + \frac{y}{\frac{3}{2}} = 1$.This simplifies to $-\frac{4x}{3} + \frac{2y}{3} = 1$.Multiplying by $3$,we get $-4x + 2y = 3$,which can be rewritten as $4x - 2y = -3$.The shaded region does not contain the origin $(0,0)$.Testing the origin $(0,0)$ in the inequality $4x - 2y \leq -3$,we get $4(0) - 2(0) \leq -3$,which means $0 \leq -3$. This is false.Since the origin does not satisfy the inequality,the shaded region represents the half-plane $4x - 2y \leq -3$.

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

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