Question

the two lines in the graph are \\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_\\_.

\\(x + y = 12\\)
\\(x + y = 8\\)

• perpendicular
• parallel

Explanation:

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<reasoning>

Convert equations to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &x + y = 12 \implies y = -x + 12\\ &x + y = 8 \implies y = -x + 8 \end{aligned}$$

\]

Compare slopes of the two lines

Using the Parallel and Perpendicular Lines knowledge point
\[

$$\begin{aligned} &m_1 = -1\\ &m_2 = -1\\ &m_1 = m_2 \end{aligned}$$

\]
</reasoning>

<answer>
The two lines in the graph are <blank>parallel</blank>.

<mcq-option>perpendicular</mcq-option>
<mcq-correct>parallel</mcq-correct>
</answer>

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Answer:

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<reasoning>

Convert equations to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &x + y = 12 \implies y = -x + 12\\ &x + y = 8 \implies y = -x + 8 \end{aligned}$$

\]

Compare slopes of the two lines

Using the Parallel and Perpendicular Lines knowledge point
\[

$$\begin{aligned} &m_1 = -1\\ &m_2 = -1\\ &m_1 = m_2 \end{aligned}$$

\]
</reasoning>

<answer>
The two lines in the graph are <blank>parallel</blank>.

<mcq-option>perpendicular</mcq-option>
<mcq-correct>parallel</mcq-correct>
</answer>

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