write an equation for a line passing through the point $(6, -6)$ that is parallel to the line $x = -1$. then write a second equation for a line passing through the point $(6, -6)$ that is perpendicular to the line $x = -1$.

the equation of the parallel line is $x = 6$.
(simplify your answer. type an equation. use integers or fractions for any numbers in the expression.)

the equation of the perpendicular line is $\square$.
(simplify your answer. type an equation. use integers or fractions for any numbers in the expression.)

Question

write an equation for a line passing through the point $(6, -6)$ that is parallel to the line $x = -1$. then write a second equation for a line passing through the point $(6, -6)$ that is perpendicular to the line $x = -1$.

the equation of the parallel line is $x = 6$.
(simplify your answer. type an equation. use integers or fractions for any numbers in the expression.)

the equation of the perpendicular line is $\square$.
(simplify your answer. type an equation. use integers or fractions for any numbers in the expression.)

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": [ "Vertical Lines", "Horizontal Lines", "Parallel and Perpendicular Lines" ], "new_concepts": [], "current_concepts": [ "Vertical Lines", "Horizontal Lines", "Parallel and Perpendicular Lines" ] } ## Analyze the given line and point Using the *Vertical Lines* knowledge point $$ \begin{aligned} &\text{Given point: } (6, -6)\ &\text{Given line: } x = -1 \quad (\text{a vertical line}) \end{aligned} $$ ## Find the parallel line equation Using the *Vertical Lines* and *Parallel and Perpendicular Lines* knowledge points $$ \begin{aligned} &\text{Parallel to vertical line } x = -1 \implies \text{must be vertical}\ &\text{Form: } x = c\ &\text{Passes through } (6, -6) \implies x = 6 \end{aligned} $$ ## Find the perpendicular line equation Using the *Horizontal Lines* and *Parallel and Perpendicular Lines* knowledge points $$ \begin{aligned} &\text{Perpendicular to vertical line } x = -1 \implies \text{must be horizontal}\ &\text{Form: } y = c\ &\text{Passes through } (6, -6) \implies y = -6 \end{aligned} $$ Write an equation for a line passing through the point $(6, -6)$ that is parallel to the line $x = -1$. Then write a second equation for a line passing through the point $(6, -6)$ that is perpendicular to the line $x = -1$. The equation of the parallel line is $x = 6$. (Simplify your answer. Type an equation. Use integers or fractions for any numbers in the expression.) The equation of the perpendicular line is $y = -6$. (Simplify your answer. Type an equation. Use integers or fractions for any numbers in the expression.) { "elements": [ { "type": "point", "params": [[6, -6]], "properties": { "name": "(6, -6)", "size": 4, "color": "#8C55F2", "withLabel": true } }, { "type": "line", "params": [[-1, -10], [-1, 10]], "properties": { "strokeColor": "#583C87", "strokeWidth": 2, "name": "x = -1", "withLabel": true } }, { "type": "line", "params": [[6, -10], [6, 10]], "properties": { "strokeColor": "#5583F2", "strokeWidth": 2, "strokeDash": 1, "name": "x = 6 (parallel)", "withLabel": true } }, { "type": "line", "params": [[-10, -6], [10, -6]], "properties": { "strokeColor": "#F2557F", "strokeWidth": 2, "strokeDash": 1, "name": "y = -6 (perpendicular)", "withLabel": true } } ], "timestamps": [0.5, 1.0, 1.5] } { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Geometry", "Parallel and Perpendicular Lines" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the given line and point

Find the parallel line equation

Find the perpendicular line equation

Answer: