Question

As part of its grand opening event, a large sporting goods store is giving out y hats each hour, x, it is open that day. The graph represents this situation. Which statement correctly describes the graph? A. The store initially has 150 hats. They give out 8 hats each hour. B. The store initially has 75 hats. They give out 8 hats each hour.C. The store initially has 600 hats. They give out 75 hats each hour. D. The store initially has 600 hats. They give out 150 hats each hour.

Answer 1

Consider the graph given

From the graph above, we see that the graph begin runs downward,

`\begin{gathered} \text{Consider the point } \\ (0,600) \\ at\text{ 0 hours},\text{ there are 600 hat} \end{gathered}`

Hence, The graph begins initially with 600 hats and then reduces to 0, by given out hat per hour.

To obtain the hat given per hour, we find the slope of the line

Where

`\begin{gathered} \text{SLope}=(\Delta y)/(\Delta x) \\ \text{Then, using the point } \\ (0,600)\text{ and (8,0)} \end{gathered}`

We have

`\begin{gathered} \text{Slope}=(y_2-y_1)/(x_2-x_1) \\ \text{Where } \\ y_2=0,y_1=600 \\ x_2=8,x_1=0 \end{gathered}`

Substituting the value, we have

`\begin{gathered} \text{Slope}=(0-600)/(8-0)=-(600)/(8)=-75 \\ \text{The negative signs shows a downward slope( giving -out)} \end{gathered}`

Hence, 75 hat wer given out per hour

Thus, the statement which correctly describes the graph is:

The store initially has 600 hats. They give out 75 hats each hour.

Answer; Option C