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 formula for direct variation 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 \( x = 5 \) (copies), substitute into \( y = kx \):
\( 1 = k \times 5 \). Solve for \( k \): \( k=\frac{1}{5} \).
Check with second data point: \( y = 5 \), \( x = 25 \). Substitute into \( y = kx \): \( 5 = k \times 25 \). Solve for \( k \): \( k=\frac{5}{25}=\frac{1}{5} \). Both give \( k = \frac{1}{5} \).

Answer:

B is incorrect. The correct answer is A. \(\frac{1}{5}\)