Answer:
The inequality for the given graph is [tex]y>\frac{2}{3}x-1[/tex].
Step-by-step explanation:
From the given graph it noticed that the line passing through (0,-1) and (3,1).
The equation of line passing through two points is defined as
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
The equation of line is
[tex]y+1=\frac{1+1}{3-0}(x-0)[/tex]
[tex]y+1=\frac{2}{3}x[/tex]
[tex]y=\frac{2}{3}x-1[/tex]
Therefore the related equation is [tex]y=\frac{2}{3}x-1[/tex].
The point (0,0) lies in the shaded region, therefore the point (0,0) is the solution of required inequality.
Put (0,0) in the related equation.
[tex]0=\frac{2}{3}(0)-1[/tex]
[tex]0=-1[/tex]
Since 0 is greater than -1, therefore the sign of inequality must be >. The related line is a dotted line, therefore we cannot use [tex]\geq[/tex].
Therefore the required inequality is
[tex]y>\frac{2}{3}x-1[/tex]
