Question

Which of the following equations shows the shaded region in the above figure?

• A. $x(y-\frac{2}{3}x)\ge 0$
• B. $x(y-\frac{3}{2}x)\ge 0$
• C. $x(y+\frac{3}{2}x)\ge 0$
• D. $x(y+\frac{2}{3}x)\ge 0$
• E. $x(y+\frac{3}{2}x)\le 0$

Answer 1

The correct option is E $x(y+\frac{3}{2}x)\le 0$

The equation of line passing through point $(-2,3)$ is $y+\frac{3}{2}x=0$
$y+\frac{3}{2}x>0$ represents region that lies right to the line $y+\frac{3}{2}x=0$ and $y+\frac{3}{2}x<0$ represents region that lies left to the line $y+\frac{3}{2}x=0$.
Therefore $x(y+\frac{3}{2}x)\le 0$ represents the shaded region.