question 6

find the equation of the line perpendicular to $y = 4x - 6$ that passes through the point $(2, -3)$ in slope-intercept form.

$y = 4x - 11$

$y = -\frac{1}{4}x - \frac{5}{2}$

$y = \frac{1}{4}x - \frac{5}{2}$

$y = -4x - 11$

Question

question 6

find the equation of the line perpendicular to $y = 4x - 6$ that passes through the point $(2, -3)$ in slope-intercept form.

$y = 4x - 11$

$y = -\frac{1}{4}x - \frac{5}{2}$

$y = \frac{1}{4}x - \frac{5}{2}$

$y = -4x - 11$

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 Conversion", "Linear Equations" ], "new_concepts": [ "Perpendicular Lines Slope" ], "current_concepts": [ "Slope-Intercept Form Conversion", "Linear Equations", "Perpendicular Lines Slope" ] } ## Determine the perpendicular slope Using the *Linear Equations* knowledge point $$ \begin{aligned} &y = 4x - 6 \implies m_1 = 4\ &m_2 = -\frac{1}{m_1} = -\frac{1}{4} \end{aligned} $$ ## Apply point-slope form Using the *Slope-Intercept Form Conversion* knowledge point $$ \begin{aligned} &y - y_1 = m_2(x - x_1)\ &y - (-3) = -\frac{1}{4}(x - 2)\ &y + 3 = -\frac{1}{4}x + \frac{1}{2} \end{aligned} $$ ## Convert to slope-intercept form Using the *Slope-Intercept Form Conversion* knowledge point $$ \begin{aligned} &y = -\frac{1}{4}x + \frac{1}{2} - 3\ &y = -\frac{1}{4}x - \frac{5}{2} \end{aligned} $$

(A) $y = 4x - 11$

(B) $y = -\frac{1}{4}x - \frac{5}{2}$

(C) $y = \frac{1}{4}x - \frac{5}{2}$

(D) $y = -4x - 11$

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

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QUESTION IMAGE

Question

Explanation:

Determine the perpendicular slope

Apply point-slope form

Convert to slope-intercept form

Answer: