what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point $(-4, -3)$?

$y + 3 = -4(x + 4)$

$y + 3 = -\frac{1}{4}(x + 4)$

$y + 3 = \frac{1}{4}(x + 4)$

$y + 3 = 4(x + 4)$

Question

what is the equation, in point-slope form, of the line that is perpendicular to the given line and passes through the point $(-4, -3)$?

$y + 3 = -4(x + 4)$

$y + 3 = -\frac{1}{4}(x + 4)$

$y + 3 = \frac{1}{4}(x + 4)$

$y + 3 = 4(x + 4)$

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 of a Line", "Perpendicular Line Equations", "Point-Slope Form" ], "new_concepts": [], "current_concepts": [ "Slope of a Line", "Perpendicular Line Equations", "Point-Slope Form" ] } ## Find slope of given line Using the **Slope of a Line** knowledge point $$ \begin{aligned} &(x_1, y_1) = (-1, 1),\quad (x_2, y_2) = (0, -3)\ &m = \frac{-3 - 1}{0 - (-1)} = \frac{-4}{1} = -4 \end{aligned} $$ ## Find perpendicular slope Using the **Perpendicular Line Equations** knowledge point $$ \begin{aligned} &m_1 \cdot m_2 = -1\ &-4 \cdot m_2 = -1 \implies m_2 = \frac{1}{4} \end{aligned} $$ ## Write point-slope equation Using the **Point-Slope Form** knowledge point $$ \begin{aligned} &(x_0, y_0) = (-4, -3),\quad m = \frac{1}{4}\ &y - y_0 = m(x - x_0)\ &y - (-3) = \frac{1}{4}(x - (-4))\ &y + 3 = \frac{1}{4}(x + 4) \end{aligned} $$

(A) $y + 3 = -4(x + 4)$

(B) $y + 3 = -\frac{1}{4}(x + 4)$

(C) $y + 3 = \frac{1}{4}(x + 4)$

(D) $y + 3 = 4(x + 4)$

{ "elements": [ { "type": "point", "params": [[-1, 1]], "properties": { "name": "(-1, 1)", "size": 3, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[0, -3]], "properties": { "name": "(0, -3)", "size": 3, "color": "#583C87", "withLabel": true } }, { "type": "point", "params": [[-4, -3]], "properties": { "name": "(-4, -3)", "size": 3, "color": "#F2557F", "withLabel": true } }, { "type": "line", "params": [[-1, 1], [0, -3]], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2 } }, { "type": "functiongraph", "params": [{"js": "0.25*(x + 4) - 3", "latex": "y = \frac{1}{4}(x + 4) - 3"}, -10, 10], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "dash": 2 } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Perpendicular Line Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Find slope of given line

Find perpendicular slope

Write point-slope equation

Answer: