select the correct answer.\nsarah wants to print copies of her artwork. at the local print shop, it costs…
select the correct answer.\nsarah 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?\na. $y = 5x$\nb. $y = \\frac{1}{5}x$\nc. $y = x$\nd. $y = \\frac{1}{25}x + 5$
Answer
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 ).