Question

katie starts a business selling organic dried chili peppers online. She decides that customers can order any number of ounces of chili peppers. The table shows some sample prices. Complete questions 16 below.

Answer 1

To answer this question, we need to check if the relationship is proportional.

We have that:

$\frac{y}{x}=k$

Then, if we have that the ratio remains the same, we have a proportional relationship:

$\begin{gathered} x=3\text{ounces,y}=\ 7.50 \\ x=5\text{ounces,}y=\ 12.50 \\ x=6ounce,y=\ 15.00 \end{gathered}$

Now, we have:

$\begin{gathered} 1\Rightarrow\frac{y}{x}=\frac{\ 7.50}{3oz}=2.5\frac{\ }{oz} \\ 2\Rightarrow\frac{y}{x}=\frac{\ 12.50}{5oz}=2.5\frac{\ }{oz} \\ 3\Rightarrow\frac{y}{x}=\frac{\ 15}{6oz}=2.5\frac{\ }{oz} \end{gathered}$

As we can see this is a proportional relationship.

To graph this relationship, we can see that it follows a linear relationship, and we know that we have this cases, the line passes through the point (0, 0). Then, the graph of this proportional relationship is:

This proportional relationship follows a linear behavior, and it can be represented by:

$undefined$

As far as we can see the graphs of the question, the graph that corresponds to the one above is Graph C since we can check that the values for x and y correspond to the ones of the table.

We found that the constant of proportionality, k, is:

$k=2.5\frac{\ }{oz}$

And we can say that the correct option is:

"B. Yes. This is a proportional relationship with k = 2.5 (in decimals). The constant of proportionality represents that the chili peppers cost $2.5 per ounce."