Problem

4. Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship. \begin{tabular}{|c|c|} \hline$s$ & $P$ \\ \hline 2 & 8 \\ \hline 3 & 12 \\ \hline 5 & 20 \\ \hline 10 & 40 \\ \hline \end{tabular} \begin{tabular}{|c|c|} \hline$d$ & $c$ \\ \hline 2 & 6.28 \\ \hline 3 & 9.42 \\ \hline 5 & 15.7 \\ \hline 10 & 31.4 \\ \hline \end{tabular} Constant of proportionality: Constant of proportionality: Equation: $P=$ Equation: $C=$

Solution

Step 1 :The constant of proportionality is the ratio between the two quantities in each table. It can be found by dividing the second quantity by the first quantity.

Step 2 :For the first table, we can divide $P$ by $s$ to find the constant of proportionality.

Step 3 :For the second table, we can divide $c$ by $d$ to find the constant of proportionality.

Step 4 :The equations representing the relationships can be written as $P = k_1 \cdot s$ and $C = k_2 \cdot d$, where $k_1$ and $k_2$ are the constants of proportionality for the first and second tables respectively.

Step 5 :The constant of proportionality for the first table is \(\boxed{4.0}\) and for the second table is \(\boxed{3.14}\).

Step 6 :The equations representing the relationships are $P = 4.0 \cdot s$ and $C = 3.14 \cdot d$.

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Source: https://solvelyapp.com/problems/46013/

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