Answer:
Shown below
Step-by-step explanation:
No graph has been plotted, but the question is answerable either way and I'll be happy to help you. In this problem, we have the following inequality:
[tex]x-y-2\geq 0[/tex]
Before we focus on getting the shaded region, let's graph the equation of the line:
[tex]x-y-2=0[/tex]
So let's write this equation in slope intercept form [tex]y=mx+6[/tex]:
STEP 1: Write the original equation.
[tex]x-y-2=0[/tex]
STEP 2: Subtract -x from both sides.
[tex]x-y-2-x=0-x \\ \\ \\ Group \ like \ terms \ on \ the \ left \ side: \\ \\ (x-x) - y-2=-x \\ \\ The \ x's \ cancel \ out \ on \ the \ left: \\ \\ -y-2=-x[/tex]
STEP 3: Add 2 to both sides.
[tex]-y-2+2=-x+2 \\ \\ -y=-x+2[/tex]
STEP 4: Multiply both sides by -1.
[tex](-1)(-y)=(-1)(-x+2) \\ \\ y=x-2[/tex]
So, [tex]m=1[/tex] and [tex]b=-2[/tex]. The graph of this line passes through these points:
[tex]If \ x=0 \ then: \\ \\ y=x-2 \therefore y=(0)-2 \therefore y=-2 \\ \\ Passes \ through \ (0,-2) \\ \\ \\ If \ y=0 \ then: \\ \\ y=x-2 \therefore 0=x-2 \therefore x=2 \\ \\ Passes \ through \ (2,0)[/tex]
By plotting this line, we get the line shown in the first figure below. To know whether the shaded region is either above or below the graph, let's take point (0,0) to test this, so from the inequality:
[tex]x-y-2\geq 0 \\ \\ Let \ x=y=0 \\ \\ 0-0-2\geq 0 \\ \\ -2\geq 0 \ False![/tex]
Since this statement is false, then the conclusion is that the region doesn't include the origin, so the shaded region is below the graph as indicated in the second figure below. The inequality includes the symbol ≥ so this means points on the line are included in the region and the line is continuous.
