8. an electrical supply store needs to order some cfl lightbulbs. the cost, $c$, in dollars, of the bulbs is $c = 6.50n + 8.76$, where $n$ is the number of bulbs purchased and $8.76$ is the postage needed.
(a) what is the $y$-intercept?
(b) does this $y$-intercept make sense in this situation? explain your answer.

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{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "y-intercept", "Linear Modeling" ], "new_concepts": [], "current_concepts": [ "y-intercept", "Linear Modeling" ] } ## Identify the y-intercept from the linear equation $$ \begin{aligned} &C = 6.50n + 8.76 \ &\text{Comparing with } y = mx + b: \ &b = 8.76 \quad \text{or} \quad (0, 8.76) \end{aligned} $$ ## Evaluate the real-world meaning of the y-intercept $$ \begin{aligned} &n = 0 \implies C = 8.76 \ &\text{This represents paying \$8.76 for postage when purchasing 0 bulbs.} \ &\text{Since a store would not order and pay postage for 0 bulbs, it does not make practical sense.} \end{aligned} $$ ## Question 8(a) $8.76$ (or the point $(0, 8.76)$) ## Question 8(b) No. It represents paying a postage cost of \$8.76 when 0 bulbs are purchased, which is not a realistic scenario for a store. { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Linear Modeling" ] }

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Explanation:

Identify the y-intercept from the linear equation

Evaluate the real-world meaning of the y-intercept

Answer:

Question 8(a)

Question 8(b)