the points (3, 24) and (7, 56) represent points of a function where y, the number of photographs, varies…
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.
Answer
Explanation:
Step1: Find the constant of variation
Since $y$ varies directly with $x$, the equation is $y = kx$. Using the point $(3,24)$, we substitute $x = 3$ and $y=24$ into the equation: $24=k\times3$, so $k=\frac{24}{3}=8$.
Step2: Check each option
Option A
For $x = 50$, $y=kx=8\times50 = 400$.
Option B
For $x = 80$, $y=8\times80=640\neq560$.
Option C
For $x = 100$, $y=8\times100 = 800\neq8000$.
Option D
For $x = 900$, $y=8\times900=7200\neq8400$.
Answer:
A. A 50 - page photo album holds 400 photographs.