Question

write an equation for the line parallel to the given line that contains c.

\\(c(4,6)\\); \\(y = -4x + 7\\)

\\(y = \\)
(type your answer in slope-intercept form.)

Explanation:

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"concepts_used": [
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<reasoning>

Identify the slope of the given line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b \\ &y = -4x + 7 \implies m = -4 \end{aligned}$$

\]

Determine the slope of the parallel line

Parallel lines have equal slopes.
\[
m_{\text{parallel}} = -4
\]

Write the equation using point-slope form

Using the Point-Slope Form knowledge point
\[

$$\begin{aligned} &y - y_1 = m(x - x_1) \\ &y - 6 = -4(x - 4) \end{aligned}$$

\]

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y - 6 = -4x + 16 \\ &y = -4x + 22 \end{aligned}$$

\]
</reasoning>

<answer>
Write an equation for the line parallel to the given line that contains C.
\(C(4,6)\); \(y = -4x + 7\)

\(y =\) <blank>\(-4x + 22\)</blank>
(Type your answer in slope-intercept form.)
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Parallel Lines Slopes"
]
}
</post_analysis>

Answer:

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"Point-Slope Form",
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<reasoning>

Identify the slope of the given line

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y = mx + b \\ &y = -4x + 7 \implies m = -4 \end{aligned}$$

\]

Determine the slope of the parallel line

Parallel lines have equal slopes.
\[
m_{\text{parallel}} = -4
\]

Write the equation using point-slope form

Using the Point-Slope Form knowledge point
\[

$$\begin{aligned} &y - y_1 = m(x - x_1) \\ &y - 6 = -4(x - 4) \end{aligned}$$

\]

Convert to slope-intercept form

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} &y - 6 = -4x + 16 \\ &y = -4x + 22 \end{aligned}$$

\]
</reasoning>

<answer>
Write an equation for the line parallel to the given line that contains C.
\(C(4,6)\); \(y = -4x + 7\)

\(y =\) <blank>\(-4x + 22\)</blank>
(Type your answer in slope-intercept form.)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Geometry",
"Parallel Lines Slopes"
]
}
</post_analysis>