The Crafty Clay Art Show has invited Troy to make and sell his famous decorative plates. He molds the plates out of clay and then paints them.

Question

There is a proportional relationship between the number of plates Troy makes, x, and the amount of clay he uses (in pounds), y.
x (plates) y (pounds)
5 15
6 18
12 36
13 39
What is the constant of proportionality? Write your answer as a whole number or decimal.
pounds per plate

Answer 1

To find the constant of proportionality between the number of plates \(x\) and the amount of clay \(y\), we need to determine how much clay is used per plate.

We can calculate the constant of proportionality (k) using the formula:

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

We can take any pair of \(x\) and \(y\) values from the provided data. Let's use the first pair: \(x = 5\) plates and \(y = 15\) pounds.

Calculating \(k\):

\[ k = \frac{15}{5} = 3 \]

Now, let's verify this with the other pairs to ensure consistency:

1. For \(x = 6\) and \(y = 18\):

\[ k = \frac{18}{6} = 3 \]

2. For \(x = 12\) and \(y = 36\):

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

3. For \(x = 13\) and \(y = 39\):

\[ k = \frac{39}{13} = 3 \]

In each case, the constant of proportionality is the same: \(k = 3\).

Thus, the constant of proportionality is

\[ \boxed{3} \]

This means Troy uses 3 pounds of clay for each plate he makes.