The quantities \[x\] and \[y\] are proportional.

\[x\]\[y\]

\[12\]

\[36\]

\[18\]

\[54\]

\[25\]

\[75\]

**Find the *constant of proportionality* \[(r)\] in the equation \[y=rx\].**

\[r = \]

When two quantities, \( x \) and \( y \), are proportional, their ratio is constant. This means that:

\[
y = r \cdot x
\]

where \( r \) is the constant of proportionality. To find \( r \), we can use any pair of corresponding values of \( x \) and \( y \). The formula for \( r \) is:

\[
r = \frac{y}{x}
\]

Let's use the first pair:

\[
r = \frac{36}{12} = 3
\]

To verify, we'll check with the other pairs:

1. For \( x = 18 \) and \( y = 54 \):
   \[
   r = \frac{54}{18} = 3
   \]

2. For \( x = 25 \) and \( y = 75 \):
   \[
   r = \frac{75}{25} = 3
   \]

Since \( r = 3 \) is consistent for all the given pairs, the constant of proportionality is:

\[
\boxed{r = 3}
\]

Would you like further details or have any questions? 

Here are some related questions:
1. What does it mean for two quantities to be directly proportional?
2. How can you determine if a set of data represents a proportional relationship?
3. If \( x = 10 \), what would \( y \) be in this proportional relationship?
4. How do proportional relationships differ from linear equations in general?
5. Can proportional relationships have a constant of proportionality that is not an integer?

**Tip:** Always check multiple pairs of values to confirm the constant of proportionality for accuracy.

The quantities [x] and [y] are proportional.

[x][y]

[12]
[36]
[18]
[54]
[25]
[75]

Find the constant of proportionality (r) in the equation [y=rx].

r = 

Learn how to find the constant of proportionality (r) from a set of proportional values for x and y. Using the equation y = rx, solve for r with step-by-step instructions. Suitable for students in Grades 6-8.

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