Answer:
The correct option is 3.
Step-by-step explanation:
If a line passing through two points, then the equation of line is
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Rel line passing through the points (0,-2) and (2,0), then related equation of red line is
[tex]y-(-2)=\frac{0-(-2)}{2-0}(x-0)[/tex]
[tex]y+2=x[/tex]
[tex]y=x-2[/tex]
Since the shaded region is above the line and the related line is a solid line therefore the sign of inequality must be ≥. The first inequality is
[tex]y\geq x-2[/tex]
Blue line passing through the points (0,2) and (4,0), then related equation of red line is
[tex]y-(2)=\frac{0-(2)}{4-0}(x-0)[/tex]
[tex]y-2=\frac{1}{2}x[/tex]
Multiply 2 on both the sides.
[tex]2y-4=x[/tex]
[tex]x+2y=4[/tex]
(0,0) is in the shaded region. So, the inequity must be satisfy by (0,0).
[tex]0+2(0)=4[/tex]
[tex]0=4[/tex]
The related line is dotted, so the required sign of inequality is <. The second inequality is
[tex]x+2y<4[/tex]
The system of linear inequalities is defined as
[tex]y\geq x-2[/tex]
[tex]x+2y<4[/tex]
Therefore the correct option is 3.
