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

Direct variation is in the form \( y = kx \), where \( k \) is the constant of variation. Here, let \( y \) be the cost (in dollars) and \( x \) be the number of copies.

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

Given \( x = 5 \) copies, \( y = \$1 \). Substitute into \( y = kx \):
\( 1 = k \times 5 \)
Solve for \( k \): \( k = \frac{1}{5} \).

Step3: Verify with second data point

For \( x = 25 \) copies, \( y = \$5 \). Using \( k = \frac{1}{5} \), check \( y = \frac{1}{5}x \):
\( \frac{1}{5} \times 25 = 5 \), which matches \( y = 5 \). So the equation is \( y = \frac{1}{5}x \).

Answer:

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