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: $C=$

Answer

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Answer

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

Steps

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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