guided example 1

determine if the two lines are parallel, perpendicular, or neither?

the slope of line a is

the slope of line b is

Question

guided example 1

determine if the two lines are parallel, perpendicular, or neither?

the slope of line a is

the slope of line b is

Accepted Answer

{ "quality": "clear", "question_count": 3, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope Formula", "Perpendicular Slopes" ], "new_concepts": [], "current_concepts": [ "Slope Formula", "Perpendicular Slopes", "Equations of Lines" ] } ## Calculate the slope of Line a $$ \begin{aligned} &\text{Points on Line } a: (0, 0), (-8, 8)\ &m_a = \frac{8 - 0}{-8 - 0} = -1 \end{aligned} $$ ## Calculate the slope of Line b $$ \begin{aligned} &\text{Points on Line } b: (0, 0), (8, 8)\ &m_b = \frac{8 - 0}{8 - 0} = 1 \end{aligned} $$ ## Determine the relationship between the lines $$ \begin{aligned} &m_a \cdot m_b = (-1) \cdot (1) = -1\ &\text{Relationship: Perpendicular} \end{aligned} $$ ## Question 1 The slope of Line a is -1 ## Question 2 The slope of Line b is 1 ## Question 3 Determine if the two lines are parallel, perpendicular, or neither? perpendicular { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Slopes" ] }

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QUESTION IMAGE

Question

Explanation:

Calculate the slope of Line a

Calculate the slope of Line b

Determine the relationship between the lines

Answer:

Question 1

Question 2

Question 3