compute the slopes for the two given functions and determine whether the functions are parallel or perpendicular.
i) $y = -5x + 20$
(ii) graph function

the given functions are parallel.
the given functions are neither parallel nor perpendicular.

Question

compute the slopes for the two given functions and determine whether the functions are parallel or perpendicular.
i) $y = -5x + 20$
(ii) graph function

the given functions are parallel.
the given functions are neither parallel nor perpendicular.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [], "current_concepts": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines", "Slope-Intercept Form" ] } ## Find the slope of the first function $$ \begin{aligned} &y = -5x + 20\ &m_1 = -5 \end{aligned} $$ ## Find the slope of the second function from the graph $$ \begin{aligned} &\text{Points on the line: } (0, 4) \text{ and } (-2, 0)\ &m_2 = \frac{4 - 0}{0 - (-2)} = \frac{4}{2} = 2 \end{aligned} $$ ## Compare the slopes to determine the relationship $$ \begin{aligned} &m_1 = -5,\quad m_2 = 2\ &m_1 e m_2 \quad (\text{not parallel})\ &m_1 \cdot m_2 = -10 e -1 \quad (\text{not perpendicular}) \end{aligned} $$

The given functions are parallel.

The given functions are neither parallel nor perpendicular.

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

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QUESTION IMAGE

Question

Explanation:

Find the slope of the first function

Find the slope of the second function from the graph

Compare the slopes to determine the relationship

Answer: