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 \( y = kx \), where \( k \) is the constant of proportionality.

Step2: Calculate \( k \) from First Data

Given \( x = 5 \) (copies), \( y = 1 \) (cost). Substitute into \( y = kx \): \( 1 = k(5) \), so \( k=\frac{1}{5} \).

Step3: Verify with Second Data

For \( x = 25 \), \( y = kx=\frac{1}{5}(25)=5 \), which matches the given cost. So the equation is \( y = \frac{1}{5}x \).

Answer:

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