find the function which is perpendicular to $x + y = 10$.

$x + y = 4$
$x - y = 10$
$x + y = 8$
all of the choices

Question

find the function which is perpendicular to $x + y = 10$.

$x + y = 4$
$x - y = 10$
$x + y = 8$
all of the choices

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Slope-Intercept Form", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Parallel and Perpendicular Lines" ] } ## Find the slope of the given line $$ \begin{aligned} x + y &= 10 \ y &= -x + 10 \ m_1 &= -1 \end{aligned} $$ ## Determine the perpendicular slope $$ \begin{aligned} m_1 \cdot m_2 &= -1 \ -1 \cdot m_2 &= -1 \ m_2 &= 1 \end{aligned} $$ ## Identify the matching option $$ \begin{aligned} &\text{Option 1: } x + y = 4 \implies y = -x + 4 \quad (m = -1) \ &\text{Option 2: } x - y = 10 \implies y = x - 10 \quad (m = 1) \ &\text{Option 3: } x + y = 8 \implies y = -x + 8 \quad (m = -1) \end{aligned} $$

(A) $x + y = 4$

(B) $x - y = 10$

(C) $x + y = 8$

(D) All of the choices

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

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QUESTION IMAGE

Question

Explanation:

Find the slope of the given line

Determine the perpendicular slope

Identify the matching option

Answer: