Answer:
The graph represent the system of linear inequalities [tex]y>\frac{1}{3}(x)+3[/tex] and [tex]3x-y>2[/tex].
Step-by-step explanation:
From the given given graph it is clear that the red line passing through the point (0,3) and (-3,2). The black line passing through the points (0,-2) and (1,1).
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 related equation of red line is
[tex]y-3=\frac{2-3}{-3}(x-0)[/tex]
[tex]y-3=\frac{1}{3}(x)[/tex]
[tex]y=\frac{1}{3}(x)+3[/tex]
The red line is dotted and shaded potion is upper side of the line, therefore the sign of inequality is >.
[tex]y>\frac{1}{3}(x)+3[/tex] .... (1)
The related equation of black line is
[tex]y-(-2)=\frac{1+2}{1-0}(x-0)[/tex]
[tex]y+2=3x[/tex]
The black line is dotted and shaded potion is lower side of the line, therefore the sign of inequality is <.
[tex]y+2<3x[/tex]
[tex]2<3x-y[/tex]
[tex]3x-y>2[/tex] .... (2)
Therefore the graph represent the system of linear inequalities [tex]y>\frac{1}{3}(x)+3[/tex] and [tex]3x-y>2[/tex].
