Answer:
The graph D represents this scenario.
Step-by-step explanation:
We know by reading the exercise that the company estimates same day delivery as a region of the miles.
We can write the same day delivery ''y'' as a region of the miles ''x'' :
[tex]y>\frac{x}{2} -3[/tex]
We need to represent this region in a graph.
One way is to find the graph of [tex]y=\frac{x}{2}-3[/tex]
This line will divide the plane into two regions. Then, using any point that verifies the original equation [tex]y>\frac{x}{2}-3[/tex] we can find the graph.
Working with the line [tex]y=\frac{x}{2}-3[/tex] ⇒
If [tex]x=0[/tex] ⇒
[tex]y=\frac{0}{2}-3\\ y=-3[/tex]
The point [tex](0,-3)[/tex] is the interception of the line with y-axis.
If [tex]y=0[/tex] ⇒ [tex]0=\frac{x}{2}-3[/tex]
[tex]\frac{x}{2}=3\\ x=6[/tex]
The point [tex](6,0)[/tex] is the interception of the line with x-axis.
We know that [tex]y>\frac{x}{2}-3[/tex] will be the region above of or below of the line [tex]y=\frac{x}{2}-3[/tex]
Now using an arbitrary point, for example [tex](0,0)[/tex] and replacing in the expression :
[tex]0>\frac{0}{2}-3\\0>-3[/tex]
The point [tex](0,0)[/tex] verifies the expression. Therefore, this point belongs to the region.
Finally, we conclude that the region is the region above of the line [tex]y=\frac{x}{2}-3[/tex] that we can write as [tex]y>\frac{x}{2}-3[/tex] and the correct option is D.
It is important to remark that given the symbol ''>'' and not ''≥'' the line doesn't belong to the region.
