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The table shows a proportional relationship between \(x\) and \(y\) with the following values:

\[
\begin{array}{c|c|c|c}
x & 1 & 2 & 3 \\
y & 3 & 6 & 9 \\
\end{array}
\]

In a proportional relationship, the ratio of \(y\) to \(x\) remains constant. To find the proportionality constant, \(k\), we calculate the ratio \( \frac{y}{x} \).

For \(x = 1\), \(y = 3\):

\[
k = \frac{y}{x} = \frac{3}{1} = 3
\]

For \(x = 2\), \(y = 6\):

\[
k = \frac{y}{x} = \frac{6}{2} = 3
\]

For \(x = 3\), \(y = 9\):

\[
k = \frac{y}{x} = \frac{9}{3} = 3
\]

In each case, the proportionality constant \(k\) is 3. Therefore, the proportionality constant (from \(y\) to \(x\)) is **3**.

Would you like more details on proportional relationships or how to apply this concept to other problems? Here are 5 related questions to expand on this:

1. How do you identify a proportional relationship from a table of values?
2. How would the proportionality constant change if one of the values in the table changed?
3. Can proportional relationships be graphed? What does the graph look like?
4. How is the proportionality constant used in solving word problems?
5. What happens if the proportional relationship involves negative numbers?

**Tip:** The constant of proportionality is the multiplier that links two variables. It's crucial for solving real-world ratio problems like speed, cost, and density calculations.

The table shows a proportional relationship between x and y. Find the proportionality constant (y to x).

Learn how to determine the proportionality constant from a table showing a direct relationship between variables x and y. This example uses a simple table to calculate the constant of proportionality k = y / x, ideal for students in Grades 6-8.

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