Answer:
The correct option is 3.
Step-by-step explanation:
From the given graph it is noticed that the related line passing through the point (-3,1) and (0,3).
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]
The equation of related line is
[tex]y-1=\frac{3-1}{0-(-3)}(x-(-3))[/tex]
[tex]y-1=\frac{2}{3}(x+3)[/tex]
[tex]y-1=\frac{2}{3}(x)+2[/tex]
Add 1 on both the sides.
[tex]y=\frac{2}{3}(x)+2+1[/tex]
[tex]y=\frac{2}{3}(x)+3[/tex]
The equation of related line is [tex]y=\frac{2}{3}(x)+3[/tex].
The related line is a dotted line, it means the point on the line does not included in the solution set.
The shaded region is above the line so the sign of inequity is >.
The required inequality is
[tex]y>\frac{2}{3}(x)+3[/tex]
Therefore option 3 is correct.
