Question

select the correct answer.
sarah wants to print copies of her artwork. at the local print shop, it costs her $1 to make 5 copies and $5 to make 25 copies. what is the constant of proportionality in this direct variation?
a. \\(\frac{1}{5}\\)
b. 5
c. 1
d. \\(\frac{1}{25}\\)

Explanation:

Step1: Recall direct variation formula

The direct variation formula is \( y = kx \), where \( k \) is the constant of proportionality, \( y \) is the cost, and \( x \) is the number of copies.

Step2: Calculate \( k \) using first data point

Given \( y = 1 \) (cost in dollars) and \( x = 5 \) (number of copies). Substitute into \( y = kx \):
\( 1 = k \times 5 \)
Solve for \( k \): \( k=\frac{1}{5}\)

Step3: Verify with second data point

For \( y = 5 \) and \( x = 25 \), substitute into \( y = kx \):
\( 5 = k \times 25 \)
Solve for \( k \): \( k=\frac{5}{25}=\frac{1}{5}\)
Both data points give \( k = \frac{1}{5} \).

Answer:

A. \(\frac{1}{5}\)