find the equation of the line that is parallel to $y = -5x - 9$ and contains the point $(-3,-3)$.

$y = ?x + \square$

Question

find the equation of the line that is parallel to $y = -5x - 9$ and contains the point $(-3,-3)$.

$y = ?x + \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": true, "concepts_used": [ "Parallel Lines", "Slope-Intercept Form", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Parallel Lines", "Slope-Intercept Form", "Linear Equations" ] } ## Identify the slope of the parallel line Using the *Parallel Lines* and *Slope-Intercept Form* knowledge points $$ \begin{aligned} &y = -5x - 9 \implies m_1 = -5\ &m_2 = m_1 = -5 \end{aligned} $$ ## Solve for the y-intercept Using the *Linear Equations* and *Slope-Intercept Form* knowledge points $$ \begin{aligned} &y = mx + b\ &-3 = -5(-3) + b\ &-3 = 15 + b\ &b = -18 \end{aligned} $$ ## Write the final equation Using the *Slope-Intercept Form* knowledge point $$ y = -5x - 18 $$ Find the equation of the line that is parallel to $y = -5x - 9$ and contains the point $(-3,-3)$. $y =$ $-5$$x +$ $-18$ { "elements": [ { "type": "functiongraph", "params": [ { "js": "-5*x - 9", "latex": "y = -5x - 9" }, -10, 10 ], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "name": "y = -5x - 9", "withLabel": true } }, { "type": "functiongraph", "params": [ { "js": "-5*x - 18", "latex": "y = -5x - 18" }, -10, 10 ], "properties": { "strokeColor": "#8C55F2", "strokeWidth": 2, "name": "y = -5x - 18", "withLabel": true } }, { "type": "point", "params": [ [-3, -3] ], "properties": { "name": "(-3, -3)", "size": 4, "color": "#F2557F", "withLabel": true } } ] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Parallel Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the slope of the parallel line

Solve for the y-intercept

Write the final equation

Answer: