what is the equation of the line that is parallel to the given line and passes through the point $(-4,-6)$?

$x = -6$
$x = -4$
$y = -6$
$y = -4$

Question

what is the equation of the line that is parallel to the given line and passes through the point $(-4,-6)$?

$x = -6$
$x = -4$
$y = -6$
$y = -4$

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": [ "Parallel Line Equations", "Slope of a Line" ], "new_concepts": [], "current_concepts": [ "Parallel Line Equations", "Slope of a Line" ] } ## Identify the equation of the given line Using the *Slope of a Line* knowledge point $$ \begin{aligned} &\text{Points on the line: } (-8, 4) \text{ and } (8, 4)\ &m = \frac{4 - 4}{8 - (-8)} = 0\ &\text{Equation: } y = 4 \end{aligned} $$ ## Determine the slope of the parallel line Using the *Parallel Line Equations* knowledge point $$ \begin{aligned} &m_{\text{parallel}} = m = 0 \end{aligned} $$ ## Find the equation of the parallel line Using the *Parallel Line Equations* knowledge point $$ \begin{aligned} &\text{Point: } (x_1, y_1) = (-4, -6)\ &y - y_1 = m_{\text{parallel}}(x - x_1)\ &y - (-6) = 0(x - (-4))\ &y = -6 \end{aligned} $$

(A) $x = -6$

(B) $x = -4$

(C) $y = -6$

(D) $y = -4$

{ "elements": [ { "type": "line", "params": [[-10, 4], [10, 4]], "properties": { "name": "y = 4", "strokeColor": "#8C55F2", "strokeWidth": 2, "withLabel": true } }, { "type": "point", "params": [[-8, 4]], "properties": { "name": "(-8, 4)", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[8, 4]], "properties": { "name": "(8, 4)", "color": "#8C55F2", "size": 3, "withLabel": true } }, { "type": "point", "params": [[-4, -6]], "properties": { "name": "(-4, -6)", "color": "#F2557F", "size": 4, "withLabel": true } }, { "type": "line", "params": [[-10, -6], [10, -6]], "properties": { "name": "y = -6", "strokeColor": "#F2557F", "strokeWidth": 2, "strokeDash": 2, "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Line Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the equation of the given line

Determine the slope of the parallel line

Find the equation of the parallel line

Answer: