Question

6 points13. The scatter plot below shows the relationship between the number ofpets that people have and the average amount they spend at the pet storeeach month. Based on the equation of the trend line, how much would youexpect someone who has 9 pets to spend at the pet store each month?

Answer 1

The correct OPTION is B.

Looking at the graph, its a straight line graph with a general equation of

`\begin{gathered} y=mx+c \\ \end{gathered}`

where y represent monthly pet store cost ($) and x represents number of pets,

and m is the gradient and c is the y-intercept.

From the plot, the y-interept is 0

To find the gradient we will consider two points:

At x=4, y=100 and x=0,y=0

`\begin{gathered} x_2=4,y_2=100\ldots..x_1=0,y_1\text{=0} \\ Gradient=\frac{y_2-y_{1_{}}}{x_2-x_1} \end{gathered}`

`\begin{gathered} \text{Gradient(m)}=(100-0)/(4-0) \\ m=(100)/(4) \\ m=25 \end{gathered}`

Now, the equation of the the line in the scatter plot is:

`\begin{gathered} y=25x+0 \\ y=25x \end{gathered}`

So to know the amount to be paid each month ($) (y) for someone with 9 pets (x) wil be calculated thus:

`\begin{gathered} y=25x \\ y=25(9) \\ y=225 \end{gathered}`

So the amount you would expect someone with 9 pets to spend at the pet store each month is $225.

Therefore, the correct OPTION is B.