The system of linear inequalities which is represented by the graph is:
y>x-2 and y<x+1
The first inequality--
It is a dotted line which passes through (-1,0) and (0,1) and the shaded region is below the line.
first we find the equation of line:
The equation of a line passing through (a,b) and (c,d) is given by:
[tex]y-b=\dfrac{d-b}{c-a}\times (x-a)[/tex]
Hence,
(a,b)=(-1,0) and (c,d)=(0,1)
Hence, the equation of line is:
[tex]y-0=\dfrac{1-0}{0-(-1)}\times (x-(-1))\\\\i.e.\\\\y=\dfrac{1}{1}\times (x+1)\\\\i.e.\\\\y=x+1[/tex]
Also, the inequality is strict since the line is dotted.
Hence, the inequality is given by: y<x+1
The second inequality --
is a dotted line which passes through (0,-2) and (2,0)
and the shaded region is above the line.
The equation of line is given by:
y=x-2
and the inequality is strict.
Hence, the inequality is given by:
y>x-2
