Question

you try!

write an equation in slope intercept form for the line that contains the point (-3, -4) and is parallel to the line y = -5x -2.

Explanation:

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</pre_analysis><reasoning>

Determine the slope of the parallel line

\[

$$\begin{aligned} &y = -5x - 2 \implies m_1 = -5 \\ &m_2 = m_1 = -5 \end{aligned}$$

\]

Use point-slope form with the given point

\[

$$\begin{aligned} &(x_1, y_1) = (-3, -4) \\ &y - y_1 = m(x - x_1) \\ &y - (-4) = -5(x - (-3)) \\ &y + 4 = -5(x + 3) \end{aligned}$$

\]

Convert to slope-intercept form

\[

$$\begin{aligned} &y + 4 = -5x - 15 \\ &y = -5x - 19 \end{aligned}$$

\]
</reasoning>
<answer>
\(y = -5x - 19\)
</answer>
<plot>
{
"elements": [
{
"type": "functiongraph",
"params": [{"js": "-5*x - 2", "latex": "y = -5x - 2"}, -10, 10],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2,
"name": "y = -5x - 2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "-5*x - 19", "latex": "y = -5x - 19"}, -10, 10],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"name": "y = -5x - 19",
"withLabel": true
}
},
{
"type": "point",
"params": [[-3, -4]],
"properties": {
"name": "(-3, -4)",
"size": 4,
"color": "#F2557F",
"strokeColor": "#F2557F",
"fillColor": "#F2557F",
"withLabel": true
}
}
]
}
</plot>
<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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"new_concepts": [
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</pre_analysis><reasoning>

Determine the slope of the parallel line

\[

$$\begin{aligned} &y = -5x - 2 \implies m_1 = -5 \\ &m_2 = m_1 = -5 \end{aligned}$$

\]

Use point-slope form with the given point

\[

$$\begin{aligned} &(x_1, y_1) = (-3, -4) \\ &y - y_1 = m(x - x_1) \\ &y - (-4) = -5(x - (-3)) \\ &y + 4 = -5(x + 3) \end{aligned}$$

\]

Convert to slope-intercept form

\[

$$\begin{aligned} &y + 4 = -5x - 15 \\ &y = -5x - 19 \end{aligned}$$

\]
</reasoning>
<answer>
\(y = -5x - 19\)
</answer>
<plot>
{
"elements": [
{
"type": "functiongraph",
"params": [{"js": "-5*x - 2", "latex": "y = -5x - 2"}, -10, 10],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2,
"name": "y = -5x - 2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "-5*x - 19", "latex": "y = -5x - 19"}, -10, 10],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2,
"name": "y = -5x - 19",
"withLabel": true
}
},
{
"type": "point",
"params": [[-3, -4]],
"properties": {
"name": "(-3, -4)",
"size": 4,
"color": "#F2557F",
"strokeColor": "#F2557F",
"fillColor": "#F2557F",
"withLabel": true
}
}
]
}
</plot>
<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>