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Let's analyze the table to determine the constant of proportionality and write the equation that represents the relationship.

The table provides pairs of values for \( s \) and \( P \):

\[
\begin{array}{c|c}
s & P \\
\hline
2 & 8 \\
3 & 12 \\
5 & 20 \\
10 & 40 \\
\end{array}
\]

To find the constant of proportionality, we can check the ratio between \( P \) and \( s \) for each pair:

\[
\frac{P}{s} = \frac{8}{2} = 4, \quad \frac{12}{3} = 4, \quad \frac{20}{5} = 4, \quad \frac{40}{10} = 4
\]

Since the ratio is constant and equal to 4, the constant of proportionality is 4.

Thus, the equation representing the proportional relationship is:
\[
P = 4s
\]

From the given options, the correct one is already selected: **P = 4s**.

Would you like further details or have any questions?

Here are 5 related questions to expand your understanding:
1. How would you solve this if the constant of proportionality was a fraction?
2. What happens to the graph of this equation?
3. Can you explain what a proportional relationship means in real-world terms?
4. How would the equation change if \( P \) was proportional to \( s^2 \) instead?
5. How would you determine the proportionality constant if the table had errors?

**Tip:** To check proportionality, always ensure that the ratio between the variables remains constant across all values.

Each table represents a proportional relationship. For each, find the constant of proportionality, and write an equation that represents the relationship. Choose the correct constant of proportionality and equation for this table: s | P 2 | 8 3 | 12 5 | 20 10 | 40

Learn how to determine the constant of proportionality and write an equation for a proportional relationship. Given the table s | P: (2, 8), (3, 12), (5, 20), (10, 40), find the correct equation P = 4s, with step-by-step reasoning. Suitable for Grades 6-8.

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