Question

The Iron-It-Out laundromat dry cleans Lila's suits.
There is a proportional relationship between the number of suits Lila dry cleans, x, and the total cost (in dollars), y.
x (suits) y (dollars)
1 $8
6 $48
7 $56
9 $72
What is the constant of proportionality? Write your answer as a whole number or decimal.

Answer 1

To find the constant of proportionality \( k \) in the relationship between the number of suits \( x \) and the total cost \( y \), we can use the formula:

\[
y = kx
\]

We can use any of the provided pairs of \( (x, y) \) to find \( k \).

Let's use the first pair \( (1, 8) \):

\[
8 = k \cdot 1 \implies k = 8
\]

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

- For \( x = 6 \):
\[
y = 8 \cdot 6 = 48 \quad \text{(which matches)}
\]

- For \( x = 7 \):
\[
y = 8 \cdot 7 = 56 \quad \text{(which matches)}
\]

- For \( x = 9 \):
\[
y = 8 \cdot 9 = 72 \quad \text{(which matches)}
\]

All pairs confirm that the constant of proportionality \( k \) is indeed:

\[
\boxed{8}
\]