unit review - functions - part 1

a hen lays 20 eggs in 4 weeks.
$\frac{20\text{ eggs}}{4\text{ weeks}} = \frac{5\text{ eggs}}{1\text{ week}}$

which graph describes this ratio?
hint: use the unit rate as the slope.

Question

unit review - functions - part 1

a hen lays 20 eggs in 4 weeks.
$\frac{20\text{ eggs}}{4\text{ weeks}} = \frac{5\text{ eggs}}{1\text{ week}}$

which graph describes this ratio?
hint: use the unit rate as the slope.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Unit Rate", "Graphing Linear Equations" ], "new_concepts": [], "current_concepts": [ "Unit Rate", "Graphing Linear Equations", "Slope-Intercept Form" ] } ## Determine the slope from the unit rate $$ \text{Slope } (m) = \text{Unit Rate} = \frac{5 \text{ eggs}}{1 \text{ week}} = 5 $$ ## Identify key coordinates on the correct graph $$ \begin{aligned} (x, y) &= (\text{Time in weeks}, \text{Eggs laid}) \ (0, 0) &\implies 0 \text{ eggs} \ (1, 5) &\implies 5 \text{ eggs} \ (2, 10) &\implies 10 \text{ eggs} \end{aligned} $$ ## Match coordinates with the given graphs $$ \begin{aligned} &\text{Graph 1 (Left): Passes through } (4, 1) \implies \text{Slope } = 0.25 \ &\text{Graph 2 (Middle): Passes through } (1, 2) \text{ and } (2, 4) \implies \text{Slope } = 2 \ &\text{Graph 3 (Right): Passes through } (1, 5) \text{ and } (2, 10) \implies \text{Slope } = 5 \end{aligned} $$

(A) Left graph (slope of 0.25)

(B) Middle graph (slope of 2)

(C) Right graph (slope of 5)

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Graphing Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Determine the slope from the unit rate

Identify key coordinates on the correct graph

Match coordinates with the given graphs

Answer: