As a young girl, Jennifer enjoyed watching her father make things in his woodworking shop. Now that she's grown up, Jennifer builds wooden furniture for a living. Her most popular product is a cedar porch swing.

Question

There is a proportional relationship between the time (in days) Jennifer spends making porch swings, x, and the number of swings she builds, y.
x (days) y (swings)
5 1
10 2
15 3
20 4
What is the constant of proportionality? Write your answer as a whole number or decimal.
swings per day

Answer 1

To find the constant of proportionality, we can use the relationship between the time spent (in days) and the number of swings built. The constant of proportionality \( k \) can be calculated using the formula:

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

Using the data points provided:

1. For \( x = 5 \) days and \( y = 1 \) swing: \[ k = \frac{1}{5} = 0.2 \]

2. For \( x = 10 \) days and \( y = 2 \) swings: \[ k = \frac{2}{10} = 0.2 \]

3. For \( x = 15 \) days and \( y = 3 \) swings: \[ k = \frac{3}{15} = 0.2 \]

4. For \( x = 20 \) days and \( y = 4 \) swings: \[ k = \frac{4}{20} = 0.2 \]

In all cases, the constant of proportionality is \( 0.2 \).

Therefore, the constant of proportionality is 0.2 swings per day.