determine whether the pair of lines is parallel, perpendicular, or neither.

$ = 3x - 8 $

$ y = 8 - x $

are the graphs of the pair of lines parallel, perpendicular, or neither?
parallel
perpendicular
neither

Question

determine whether the pair of lines is parallel, perpendicular, or neither.

$ = 3x - 8 $

$ y = 8 - x $

are the graphs of the pair of lines parallel, perpendicular, or neither?
parallel
perpendicular
neither

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Parallel and Perpendicular Lines" ] } ## Identify the slope of the first line Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = 3x - 8\ &m_1 = 3 \end{aligned} $$ ## Identify the slope of the second line Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = 8 - x = -1x + 8\ &m_2 = -1 \end{aligned} $$ ## Compare the slopes Using the *Parallel and Perpendicular Lines* knowledge point $$ \begin{aligned} &m_1 e m_2 \implies 3 e -1 \quad \text{(Not parallel)}\ &m_1 \cdot m_2 e -1 \implies 3 \cdot (-1) = -3 e -1 \quad \text{(Not perpendicular)} \end{aligned} $$

Parallel

Perpendicular

Neither

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Parallel and Perpendicular Lines" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Identify the slope of the first line

Identify the slope of the second line

Compare the slopes

Answer: