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.
a 100 - page photo album holds 8, 000 photographs.
a 900 - page photo album holds 8, 400 photographs.
an 80 - page photo album holds 560 photographs.

Explanation:

Step1: Find the direct variation equation

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

• Option 1 (50 - page, 400 photos): Substitute \( x = 50 \) into \( y = 8x \): \( y = 8\times50 = 400 \). This matches.
• Option 2 (100 - page, 8000 photos): \( y = 8\times100 = 800

eq 8000 \).

• Option 3 (900 - page, 8400 photos): \( y = 8\times900 = 7200

eq 8400 \).

• Option 4 (80 - page, 560 photos): \( y = 8\times80 = 640

eq 560 \).

Answer:

A 50 - page photo album holds 400 photographs.