Question

the points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies directly with x, the number of pages in an album. which statement describes another point on the graph of this function?
a 50 - page photo album holds 400 photographs.
an 80 - page photo album holds 560 photographs.
a 100 - page photo album holds 8,000 photographs.
a 900 - page photo album holds 8,400 photographs.

Explanation:

Step1: Find the constant of proportionality

Since \( y \) varies directly with \( x \), the equation is \( y = kx \). Using the point \((3, 24)\), substitute \( x = 3 \) and \( y = 24 \) into the equation: \( 24 = k \times 3 \). Solve for \( k \): \( k=\frac{24}{3}=8 \). So the equation is \( y = 8x \).

Step2: Check each option

• For option A: \( x = 50 \), then \( y = 8\times50 = 400 \). This matches the statement.
• For option B: \( x = 80 \), \( y = 8\times80 = 640

eq560 \).

• For option C: \( x = 100 \), \( y = 8\times100 = 800

eq8000 \).

• For option D: \( x = 900 \), \( y = 8\times900 = 7200

eq8400 \).

Answer:

A. A 50 - page photo album holds 400 photographs.