which statement explains how the lines $x - y = 2$ and $y = x + 1$ are related?

they are parallel.
they are perpendicular.
they are the same line.
they are not related.

Question

which statement explains how the lines $x - y = 2$ and $y = x + 1$ are related?

they are parallel.
they are perpendicular.
they are the same line.
they are not related.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Linear Functions", "Perpendicular Lines" ], "new_concepts": [ "Parallel Lines" ], "current_concepts": [ "Linear Functions", "Perpendicular Lines", "Parallel Lines" ] } ## Convert first equation to slope-intercept form $$ \begin{aligned} x - y &= 2 \ -y &= -x + 2 \ y &= x - 2 \end{aligned} $$ ## Compare slopes of both lines $$ \begin{aligned} y_1 &= x - 2 \implies m_1 = 1 \ y_2 &= x + 1 \implies m_2 = 1 \end{aligned} $$ ## Determine geometric relationship $$ \begin{aligned} &m_1 = m_2 = 1 \ &b_1 = -2 e b_2 = 1 \ &\text{Since slopes are equal and } y\text{-intercepts are different, the lines are parallel.} \end{aligned} $$

They are parallel.

They are perpendicular.

They are the same line.

They are not related.

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QUESTION IMAGE

Question

Explanation:

Convert first equation to slope-intercept form

Compare slopes of both lines

Determine geometric relationship

Answer: