which lines in the graph have a slope greater than 1 but less than 2?

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Slope of a Line", "Linear Graphs" ], "current_concepts": [ "Slope of a Line", "Linear Graphs" ] } ## Calculate the slope of each line from the origin to its endpoint $$ \begin{aligned} &m_1 = \frac{6}{2} = 3 \ &m_2 = \frac{6}{3} = 2 \ &m_3 = \frac{6}{4} = 1.5 \ &m_4 = \frac{6}{5} = 1.2 \ &m_5 = \frac{6}{6} = 1 \end{aligned} $$ ## Identify slopes strictly between 1 and 2 $$ \begin{aligned} &1 < m < 2 \ &1 < 1.5 < 2 \implies \text{Line 3} \ &1 < 1.2 < 2 \implies \text{Line 4} \end{aligned} $$ Lines 3 and 4 { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Slope of a Line" ] }

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Explanation:

Calculate the slope of each line from the origin to its endpoint

Identify slopes strictly between 1 and 2

Answer: