Answer:
The system of inequalities is
[tex]y<-x-2[/tex]
[tex]y>0.25x[/tex]
Step-by-step explanation:
step 1
Find the equation of the dashed line with negative slope
The line passes through the points
(0,-2) and (-2,0)
Find the slope
[tex]m=(0+2)/(-2-0)=-1[/tex]
Find the equation of the line in slope intercept form
[tex]y=mx+b[/tex]
we have
[tex]m=-1\\b=-2[/tex]
substitute
[tex]y=-x-2[/tex]
The solution of the inequality is the shaded area below the dashed line
therefore
The equation of the inequality A is
[tex]y<-x-2[/tex]
step 2
Find the equation of the dashed line with positive slope
The line passes through the points
(0,0) and (4,1)
Find the slope
[tex]m=(1-0)/(4-0)=0.25[/tex]
Find the equation of the line (direct variation)
[tex]y=kx[/tex]
we have
[tex]k=0.25[/tex]
substitute
[tex]y=0.25x[/tex]
The solution of the inequality is the shaded area above the dashed line
therefore
The equation of the inequality B is
[tex]y>0.25x[/tex]
therefore
The system of inequalities is
[tex]y<-x-2[/tex]
[tex]y>0.25x[/tex]
