Answer:
see the explanation
Step-by-step explanation:
From the graph take two points
we have
(-1,4) and (1,1)
Find the slope
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute
[tex]m=\frac{1-4}{1+1}[/tex]
[tex]m=-\frac{3}{2}[/tex]
Find the equation of the solid line in slope point form
[tex]y-y1=m(x-x1)[/tex]
we have
[tex]m=-\frac{3}{2}[/tex]
[tex]point\ (1,1)[/tex]
substitute
[tex]y-1=-\frac{3}{2}(x-1)[/tex]
isolate the variable y
[tex]y-1=-\frac{3}{2}x+\frac{3}{2}[/tex]
[tex]y=-\frac{3}{2}x+\frac{5}{2}[/tex]
[tex]y=-1.5x+2.5[/tex]
The solution of the inequality is the shaded area below the solid line
so
The equation of the inequality is
[tex]y\leq -1.5x+2.5[/tex]
The solution is the shaded area below the solid line [tex]y=-1.5x+2.5[/tex]
All points belonging to the shaded area including the boundary line are part of the solution of the inequality
Example
point (0,2.5)
substitute in the inequality
[tex]2.5\leq -1.5(0)+2.5[/tex]
[tex]2.5\leq 2.5[/tex] ----> is true
therefore
The point hold true for the inequality
