Decide whether each table could represent a proportional...

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality? a. Annie's Attic is giving away $\$ 5$ off coupons. \begin{tabular}{|c|c|} \hline original price & sale price \\ \hline$\$ 15$ & $\$ 10$ \\ \hline$\$ 25$ & $\$ 20$ \\ \hline$\$ 35$ & $\$ 30$ \\ \hline \end{tabular} b. Bettie's Boutique is having a $20 \%$ off sale. \begin{tabular}{|c|c|} \hline original price & sale price \\ \hline$\$ 15$ & $\$ 12$ \\ \hline$\$ 25$ & $\$ 20$ \\ \hline$\$ 35$ & $\$ 28$ \\ \hline \end{tabular}

Decide whether each table could represent a proportional relationship. If the relationship could be proportional, what would be the constant of proportionality?
a. Annie's Attic is giving away $\$ 5$ off coupons.
\begin{tabular}{|c|c|}
\hline original price & sale price \\
\hline$\$ 15$ & $\$ 10$ \\
\hline$\$ 25$ & $\$ 20$ \\
\hline$\$ 35$ & $\$ 30$ \\
\hline
\end{tabular}
b. Bettie's Boutique is having a $20 \%$ off sale.
\begin{tabular}{|c|c|}
\hline original price & sale price \\
\hline$\$ 15$ & $\$ 12$ \\
\hline$\$ 25$ & $\$ 20$ \\
\hline$\$ 35$ & $\$ 28$ \\
\hline
\end{tabular}

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Key Concepts

Proportional Relationship

A proportional relationship is one in which two quantities maintain a consistent ratio. This means that as one quantity changes, the other changes at a constant rate, and the relationship can be represented by the equation y = kx, where k is a fixed constant. Proportional relationships produce straight-line graphs that pass through the origin.

Constant of Proportionality

The constant of proportionality is the factor by which one quantity is multiplied to obtain the corresponding quantity in a proportional relationship. It is calculated by dividing the output value by the input value (y/x) and remains the same for all pairs of values in the relationship.

Ratio

A ratio is a comparison between two quantities that expresses how many times one value contains another. In the context of proportional relationships, it represents the consistent relationship between the two variables, and if the ratio remains unchanged across different pairs of values, the relationship is proportional.

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