Question

Every Sunday, Devon and her cousins get together for brunch. This week, Devon is in charge of making fresh-squeezed orange juice.
There is a proportional relationship between the number of oranges Devon squeezes, x, and the amount of juice (in ounces) she makes, y.
x (oranges) y (ounces)
2 6
3 9
4 12
6 18
What is the constant of proportionality? Write your answer as a whole number or decimal.
ounces per orange

Answer 1

To find the constant of proportionality \( k \), we can use the values from the proportional relationship \( y = kx \). We can rearrange this to find \( k = \frac{y}{x} \).

Using the pairs you provided, we can calculate \( k \) for each pair:

1. For \( x = 2 \) and \( y = 6 \):
\[
k = \frac{6}{2} = 3
\]

2. For \( x = 3 \) and \( y = 9 \):
\[
k = \frac{9}{3} = 3
\]

3. For \( x = 4 \) and \( y = 12 \):
\[
k = \frac{12}{4} = 3
\]

4. For \( x = 6 \) and \( y = 18 \):
\[
k = \frac{18}{6} = 3
\]

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

Thus, the constant of proportionality (ounces per orange) is **3**.