the two lines in the graph are \_\_\_\_\_\_\_\_\_\_\_\_.

$x + y = 12$
$x + y = 8$

* perpendicular
* parallel

Question

the two lines in the graph are \_\_\_\_\_\_\_\_\_\_\_\_.

$x + y = 12$
$x + y = 8$

* perpendicular
* parallel

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" ] } ## Convert equations to slope-intercept form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &x + y = 12 \implies y = -x + 12\ &x + y = 8 \implies y = -x + 8 \end{aligned} $$ ## Compare slopes of the two lines Using the *Parallel and Perpendicular Lines* knowledge point $$ \begin{aligned} &m_1 = -1\ &m_2 = -1\ &m_1 = m_2 \end{aligned} $$ The two lines in the graph are parallel. perpendicular

parallel

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

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QUESTION IMAGE

Question

Explanation:

Convert equations to slope-intercept form

Compare slopes of the two lines

Answer: