Question

One company estimates same day delivery as more than three less than half the total number of miles which graph represents this scenario?
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Answer 1

Answer:

Let Same day delivery charge =$ y

If number of miles traveled =x Miles

So,the statement,Same day delivery charge as more than three less than half the total number of miles, in terms of inequality can be Written as

  $y>\frac{x}{2}-3\\\\\rightarrow -y+\frac{x}{2}>3\\\\-2y+x>6\\\\\frac{x}{6}+\frac{y}{-3}>1$

 Option D

Answer 2

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'' :

$y>\frac{x}{2} -3$

We need to represent this region in a graph.

One way is to find the graph of $y=\frac{x}{2}-3$

This line will divide the plane into two regions. Then, using any point that verifies the original equation $y>\frac{x}{2}-3$ we can find the graph.

Working with the line $y=\frac{x}{2}-3$ ⇒

If $x=0$ ⇒

$y=\frac{0}{2}-3\\ y=-3$

The point $(0,-3)$ is the interception of the line with y-axis.

If $y=0$ ⇒ $0=\frac{x}{2}-3$

                              $\frac{x}{2}=3\\ x=6$

The point $(6,0)$ is the interception of the line with x-axis.

We know that $y>\frac{x}{2}-3$ will be the region above of or below of the line $y=\frac{x}{2}-3$

Now using an arbitrary point, for example $(0,0)$ and replacing in the expression :

$0>\frac{0}{2}-3\\0>-3$

The point $(0,0)$ verifies the expression. Therefore, this point belongs to the region.

Finally, we conclude that the region is the region above of the line $y=\frac{x}{2}-3$ that we can write as $y>\frac{x}{2}-3$ 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.