Answer: The correct option is B.
Explanation:
The given inequalities are,
[tex]y\leq x-2[/tex]
[tex]y\geq \frac{1}{4}x-4[/tex]
The relative equation of (1) inequality is,
[tex]y= x-2[/tex]
At x=0, we get y=-2 and x=1, we get y=-1.
Check the first inequality by origin (0,0).
[tex]0\leq 0-2[/tex]
[tex]0\leq -2[/tex]
This statement is false therefore the the point (0,0) not lies in the shade area of [tex]y\leq x-2[/tex].
The relative equation of (2) inequality is,
[tex]y=\frac{1}{4}x-4[/tex]
At x=0, we get y=-4 and x=4, we get y=-3.
Check the first inequality by origin (0,0).
[tex]0\geq \frac{1}{4}(0)-4[/tex]
[tex]0\geq -4[/tex]
This statement is true therefore the the point (0,0) will lies in the shade area of [tex]y\geq \frac{1}{4}x-4[/tex].
From the graph we can say that the common shade region is B.
