find the equation of the line that passes through the point $(4, -1)$ and is perpendicular to $y = x + 2$

$y = -x + 1$
$y = -x + 3$
$y = x$
$y = x - 2$

Question

find the equation of the line that passes through the point $(4, -1)$ and is perpendicular to $y = x + 2$

$y = -x + 1$
$y = -x + 3$
$y = x$
$y = x - 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Slope-Intercept Form", "Perpendicular Lines Slopes", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope-Intercept Form", "Perpendicular Lines Slopes", "Point-Slope Form" ] } ## Identify the slope of the given line Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = x + 2\ &m_1 = 1 \end{aligned} $$ ## Determine the perpendicular slope Using the *Perpendicular Lines Slopes* knowledge point $$ \begin{aligned} &m_1 \cdot m_2 = -1\ &1 \cdot m_2 = -1\ &m_2 = -1 \end{aligned} $$ ## Write the equation using the given point Using the *Point-Slope Form* knowledge point $$ \begin{aligned} &(x_1, y_1) = (4, -1)\ &y - y_1 = m_2(x - x_1)\ &y - (-1) = -1(x - 4)\ &y + 1 = -x + 4 \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form* knowledge point $$ \begin{aligned} &y = -x + 4 - 1\ &y = -x + 3 \end{aligned} $$

(A) $y = -x + 1$

(B) $y = -x + 3$

(C) $y = x$

(D) $y = x - 2$

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QUESTION IMAGE

Question

Explanation:

Identify the slope of the given line

Determine the perpendicular slope

Write the equation using the given point

Convert to slope-intercept form

Answer: