compute the slopes for the two given functions and determine whether the lines are parallel or perpendicular. (i)$y = 4x + 20$ (ii) line in the graph

the given lines are parallel.
the given lines are perpendicular.

Question

compute the slopes for the two given functions and determine whether the lines are parallel or perpendicular. (i)$y = 4x + 20$ (ii) line in the graph

the given lines are parallel.
the given lines are perpendicular.

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", "Slope of a Linear Function", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Slope of a Linear Function", "Parallel and Perpendicular Lines" ] } ## Find slope of first line Using the *Slope-Intercept Form* and *Slope of a Linear Function* knowledge points $$ \begin{aligned} &y = 4x + 20\ &m_1 = 4 \end{aligned} $$ ## Find slope of second line Using the *Slope of a Linear Function* knowledge point $$ \begin{aligned} &(x_1, y_1) = (0, 1)\ &(x_2, y_2) = (-1, -3)\ &m_2 = \frac{-3 - 1}{-1 - 0} = \frac{-4}{-1} = 4 \end{aligned} $$ ## Compare slopes Using the *Parallel and Perpendicular Lines* knowledge point $$ \begin{aligned} &m_1 = m_2 = 4\ &\text{Lines are parallel.} \end{aligned} $$

The given lines are parallel.

The given lines are perpendicular.

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

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QUESTION IMAGE

Question

Explanation:

Find slope of first line

Find slope of second line

Compare slopes

Answer: