Answer:
Option C.
Step-by-step explanation:
If a line passes through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex], then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
From the given graph it is clear that the related line passes thorough the points (0,2.5) and (2,-1.5).
The equation of related line is
[tex]y-2.5=\frac{-1.5-2.5}{2-0}(x-0)[/tex]
[tex]y-2.5=\frac{-4}{2}(x)[/tex]
[tex]y-2.5=-2x[/tex]
Add 2.5 on both sides.
[tex]y-2.5+2.5=-2x+2.5[/tex]
[tex]y=-2x+2.5[/tex]
Th sign of inequality is either ≤ or ≥ because the related line is a solid line. It means the points on the line are included in the solution set.
Let the required inequality is
[tex]y\geq -2x+2.5[/tex]
(1,1) is included in the shaded region. So, the above inequality is true for (1,1).
[tex]1\geq -2(1)+2.5[/tex]
[tex]1\geq 0.5[/tex]
The assumed inequality is true for (1,1). So, the required inequality isn [tex]y\geq -2x+2.5[/tex].
Therefore, the correct option is C.
