Answer: The correct option is A.
Explanation:
From the given figure it is noticed that at y = -3 there is dotted line and the it shaded in upward direction.
Since it is a dotted line -3 will not included. It means it will take all value of y which are more than -3.
[tex]y>-3[/tex] ......(1)
The second line passing through the origin, slope is negative and change in y is same as change in x, therefore the equation of line is y = -x.
The line shaded downwards it means all the point in shaded region will satisfies the inequality.
The point (-5,1) is in shaded region. check this point for the line y=-x
[tex]1=-(-5)[/tex]
[tex]1=5[/tex]
We know that 1 is less than 5 and it is not a dotted line it means the sign of inequality is less than or equal to. so, the equation is,
[tex]y\leq x[/tex]
Therefore, the correct option is A.
