Question

The Crafty Clay Art Show has invited Sofia to make and sell her famous decorative plates. She molds the plates out of clay and then paints them.
There is a proportional relationship between the number of plates Sofia makes, x, and the amount of clay she uses (in pounds), y.
x (plates) y (pounds)
5 10
6 12
7 14
10 20
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, we can determine the amount of clay used (y) for each plate made (x). The constant of proportionality (k) can be calculated using the formula:

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

Let's calculate it for one of the pairs. I'll take the first pair of numbers:

For \( x = 5 \) plates and \( y = 10 \) pounds:

\[ k = \frac{10}{5} = 2 \]

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

1. For \( x = 6 \) plates and \( y = 12 \) pounds:
\[ k = \frac{12}{6} = 2 \]

2. For \( x = 7 \) plates and \( y = 14 \) pounds:
\[ k = \frac{14}{7} = 2 \]

3. For \( x = 10 \) plates and \( y = 20 \) pounds:
\[ k = \frac{20}{10} = 2 \]

In each case, the constant of proportionality is the same. Therefore, the constant of proportionality is:

**2 pounds per plate**.