find the equation of the line that is parallel to $y = -6x + 3$ and contains the point $(-2,16)$.

$y = ?x + \square$

Question

find the equation of the line that is parallel to $y = -6x + 3$ and contains the point $(-2,16)$.

$y = ?x + \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Parallel Line Slopes", "Point-Slope Form", "Slope-Intercept Form" ], "current_concepts": [ "Parallel Line Slopes", "Point-Slope Form", "Slope-Intercept Form" ] } ## Identify the slope of the parallel line $$ \begin{aligned} &y = -6x + 3 \implies m_1 = -6\ &m_2 = m_1 = -6 \end{aligned} $$ ## Use the point-slope formula to find the equation $$ \begin{aligned} &y - y_1 = m(x - x_1)\ &y - 16 = -6(x - (-2))\ &y - 16 = -6(x + 2) \end{aligned} $$ ## Convert to slope-intercept form $$ \begin{aligned} &y - 16 = -6x - 12\ &y = -6x + 4 \end{aligned} $$ Find the equation of the line that is parallel to $y = -6x + 3$ and contains the point $(-2,16)$. $y =$ $-6$$x +$ $4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Slope-Intercept Form" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the slope of the parallel line

Use the point-slope formula to find the equation

Convert to slope-intercept form

Answer: