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. \boxed{} pounds per plate submit

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Using \( x = 5 \) and \( y = 10 \), we substitute into the formula: \( k=\frac{y}{x}=\frac{10}{5} \)
\( \frac{10}{5}=2 \)

We can verify with other pairs. For \( x = 6 \), \( y = 12 \): \( \frac{12}{6}=2 \), for \( x = 7 \), \( y = 14 \): \( \frac{14}{7}=2 \), and for \( x = 10 \), \( y = 20 \): \( \frac{20}{10}=2 \). All give \( k = 2 \).

Answer:

2