For this case, we find the equation of the line of the form:
[tex]y = mx + b[/tex]
Where:
[tex]m = \frac {y2-y1} {x2-x1} = \frac {-3-0} {0 - (- 3)} = \frac {-3} {3} = - 1[/tex]
So, we have:
[tex]y = -x + b[/tex]
We substitute one of the points:[tex]0 = - (- 3) + b\\0 = 3 + b\\b = -3[/tex]
Thus, the equation is:
[tex]y = -x-3[/tex]
Now, we substitute a point belonging to the region to determine the sign.
([tex](0,0)\\0? - (0) -3\\0? -3[/tex]
-3 is less than 0.
Then, the inequality is:
[tex]y> -x-3[/tex]
As the border of the region is dotted, then it remains ">."
Answer:
[tex]y> -x-3[/tex]
