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. what is the constant of proportionality in this direct variation?\na. \\(\\frac{1}{5}\\)\nb. 5\nc. 1\nd. \\(\\frac{1}{25}\\)

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. what is the constant of proportionality in this direct variation?\na. \\(\\frac{1}{5}\\)\nb. 5\nc. 1\nd. \\(\\frac{1}{25}\\)

Answer

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})