We need to find the system of inequalities modeled by the graph.
At first, we will find the equations of the lines:
The general equation of the line is : y = mx + b
where m is the slope and b is y - intercept
The equation of the red solid line:
the line passing through the points (-2 , 0) and (0,4)
The slope = rise/run = 4/2 = 2
b = y- intercept = 4
so, the equation of the line is : y = 2x + 4
As the shaded area on the left of the line, the inequality will be:
[tex]y\ge2x+4[/tex]
Now, finding the equation of the dash blue line:
The line passing through the points ( 4 , 0 ) , ( 0 , 4 )
The slope = rise/run = 4/-4 = -1
b = y- intercept = 4
so, the equation of the line is : y = -x + 4
So, the inequality will be:
[tex]y<-x+4[/tex]
So, the system of inequalities modeled by the graph is:
[tex]\begin{gathered} y\ge2x+4 \\ y<-x+4 \end{gathered}[/tex]
So, the answer is option A.
