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. which equation represents this direct variation?
a. $y = 5x$
b. $y = \frac{1}{5}x$
c. $y = x$
d. $y = \frac{1}{25}x + 5$

Explanation:

Step1: Recall direct variation formula

The formula for direct variation is \( y = kx \), where \( k \) is the constant of variation.

Step2: Calculate constant \( k \)

We know that when \( x = 5 \) (copies), \( y = 1 \) (dollar). Substitute into \( y = kx \):
\( 1 = k \times 5 \)
Solve for \( k \): \( k = \frac{1}{5} \).

Step3: Form the equation

Using \( k = \frac{1}{5} \) in \( y = kx \), we get \( y = \frac{1}{5}x \). We can verify with \( x = 25 \), \( y = \frac{1}{5} \times 25 = 5 \), which matches the given information.

Answer:

B. \( y = \frac{1}{5}x \)