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.

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.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Direct Variation" ], "new_concepts": [], "current_concepts": [ "Direct Variation", "Linear Modeling" ] } ## Find the constant of variation $$ \begin{aligned} y &= kx \ 24 &= k(3) \ k &= 8 \ 56 &= 8(7) \quad \text{(verified)} \end{aligned} $$ ## Test the given options using the model $$ \begin{aligned} &\text{Option A: } x = 50 \implies y = 8(50) = 400 \quad \text{(True)} \ &\text{Option B: } x = 80 \implies y = 8(80) = 640 e 560 \ &\text{Option C: } x = 100 \implies y = 8(100) = 800 e 8000 \ &\text{Option D: } x = 900 \implies y = 8(900) = 7200 e 8400 \end{aligned} $$

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

(B) An 80-page photo album holds 560 photographs.

(C) A 100-page photo album holds 8,000 photographs.

(D) A 900-page photo album holds 8,400 photographs.

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Direct Variation" ] }

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Question

Explanation:

Find the constant of variation

Test the given options using the model

Answer: