https://file.aiquickdraw.com/mathbot/file/172866913837591ybpeyx.jpg

The table in the image shows values of \( x \) and \( y \) that form a proportional relationship. The data given is:

\[
\begin{array}{|c|c|}
\hline
x & y \\
\hline
1 & 3.5 \\
2 & 7 \\
4.5 & 15.75 \\
\hline
\end{array}
\]

In a proportional relationship, the ratio \( \frac{y}{x} \) remains constant. Let’s check if the ratio is the same for all pairs.

For \( x = 1 \) and \( y = 3.5 \):

\[
\frac{y}{x} = \frac{3.5}{1} = 3.5
\]

For \( x = 2 \) and \( y = 7 \):

\[
\frac{y}{x} = \frac{7}{2} = 3.5
\]

For \( x = 4.5 \) and \( y = 15.75 \):

\[
\frac{y}{x} = \frac{15.75}{4.5} = 3.5
\]

Since the ratio \( \frac{y}{x} = 3.5 \) is constant for all the given pairs, this confirms that the relationship is proportional.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do we determine if a relationship is proportional?
2. Can you explain why the ratio \( \frac{y}{x} \) is key in proportional relationships?
3. What would happen if one pair in the table had a different ratio?
4. How do you find the constant of proportionality from a table of values?
5. Can proportional relationships be represented as linear equations?

**Tip:** To check proportionality, always divide \( y \) by \( x \) for each pair of values and verify that the ratio stays the same.

The table below shows values that stand in a proportional relationship. Select one value from the table that is equal to the constant of proportionality.

Learn how to determine the constant of proportionality using a table of values. In this problem, the values of x and y form a proportional relationship, and the ratio y/x remains constant. Suitable for students in Grades 6-8.

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