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

\y = -\frac{5}{8}x - 3\
\y = -\frac{5}{8}x + 3\

choose the correct answer below.
a. perpendicular
b. parallel
c. neither

Question

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

\y = -\frac{5}{8}x - 3\
\y = -\frac{5}{8}x + 3\

choose the correct answer below.
a. perpendicular
b. parallel
c. 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 slopes of both lines Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &\text{Line 1: } y = -\frac{5}{8}x - 3 \implies m_1 = -\frac{5}{8}\ &\text{Line 2: } y = -\frac{5}{8}x + 3 \implies m_2 = -\frac{5}{8} \end{aligned} $$ ## Compare the slopes and y-intercepts Using the *Parallel and Perpendicular Lines* knowledge point $$ \begin{aligned} &m_1 = m_2 = -\frac{5}{8}\ &b_1 = -3 e b_2 = 3 \end{aligned} $$ Since the slopes are equal and the y-intercepts are different, the lines are parallel.

(A) Perpendicular

(B) Parallel

(C) Neither

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

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QUESTION IMAGE

Question

Explanation:

Identify the slopes of both lines

Compare the slopes and y-intercepts

Answer: