find the function which is parallel to $5x - 2y = 10$.

$2x - 5y = 10$
$2x + 5y = 10$
$20x - 8y = 60$
all of the choices

Question

find the function which is parallel to $5x - 2y = 10$.

$2x - 5y = 10$
$2x + 5y = 10$
$20x - 8y = 60$
all of the choices

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 of a Linear Function", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope of a Linear Function", "Parallel and Perpendicular Lines" ] } ## Find the slope of the given line Using the **Slope of a Linear Function** knowledge point $$ \begin{aligned} 5x - 2y &= 10 \ -2y &= -5x + 10 \ y &= \frac{5}{2}x - 5 \ m_1 &= \frac{5}{2} \end{aligned} $$ ## Determine the slope of a parallel line Using the **Parallel and Perpendicular Lines** knowledge point $$ m_2 = m_1 = \frac{5}{2} $$ ## Analyze the given options Using the **Slope of a Linear Function** knowledge point $$ \begin{aligned} &\text{Option 1: } 2x - 5y = 10 \implies y = \frac{2}{5}x - 2 \implies m = \frac{2}{5} \ &\text{Option 2: } 2x + 5y = 10 \implies y = -\frac{2}{5}x + 2 \implies m = -\frac{2}{5} \ &\text{Option 3: } 20x - 8y = 60 \implies -8y = -20x + 60 \implies y = \frac{5}{2}x - \frac{15}{2} \implies m = \frac{5}{2} \end{aligned} $$

(A) $2x - 5y = 10$

(B) $2x + 5y = 10$

(C) $20x - 8y = 60$

(D) All of the choices

{ "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 given line

Determine the slope of a parallel line

Analyze the given options

Answer: