Answer:
The required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].
Step-by-step explanation:
From the given graph it is clear that the related line passes through the points (-3,-3) and (3,1).
If a line passes through two points, then the equation of line is
[tex]y-y_1=\frac{y-y_1}{x-x_1}(x-x_1)[/tex]
The equation of related line is
[tex]y-(-3)=\frac{1-(-3)}{3-(-3)}(x-(-3))[/tex]
[tex]y+3=\frac{4}{6}(x+3)[/tex]
[tex]y+3=\frac{2}{3}(x+3)[/tex]
[tex]y+3=\frac{2}{3}(x)+2[/tex]
Subtract 3 from both the sides.
[tex]y=\frac{2}{3}(x)+2-3[/tex]
[tex]y=\frac{2}{3}(x)-1[/tex]
The equation of related line is [tex]y=\frac{2}{3}(x)-1[/tex]. The related line is a dotted and the shaded region is below the line. So, the sign of inequality is <.
The required inequality is
[tex]y<\frac{2}{3}(x)-1[/tex]
Therefore the required inequality is [tex]y<\frac{2}{3}(x)-1[/tex].
