Answer:
The system of linear inequalities represented by the graph is:
y > (2/3) x + 3 and y <= - (1/3) x + 2
Explanation:
In the graph we can see the region on and below the red line, and above the black dashed line.
1) The red line goes through the points:
P1=(0,2)=(x1,y1)→x1=0, y1=2
P2=(3,1)=(x2,y2)→x2=3, y2=1
The slope of this line is:
s=(y2-y1)/(x2-x1)
Replacing the known values:
s=(1-2)/(3-0)
s=(-1)/(3)
s=-(1/3)
The equation of the red line is:
y-y1=s(x-x1)
y-2=-(1/3)(x-0)
y-2=-(1/3)x
y-2+2=-(1/3)x+2
y=-(1/3)x+2
The area on and below the red line is: y<=-(1/3)x+2
2) The black dashed line goes through the points:
P1=(-3,1)=(x1,y1)→x1=-3, y1=1
P2=(0,3)=(x2,y2)→x2=0, y2=3
The slope of this line is:
s=(y2-y1)/(x2-x1)
Replacing the known values:
s=(3-1)/(0-(-3))
s=(2)/(0+3)
s=(2)/(3)
s=(2/3)
The equation of the red line is:
y-y2=s(x-x2)
y-3=(2/3)(x-0)
y-3=(2/3)x
y-3+3=(2/3)x+3
y=(2/3)x+3
The area above the black dashed line is: y>(2/3)x+3
Then, the system of linear inequalities represented by the graph is:
y>(2/3)x+3 and y<=-(1/3)x+2