Question

1. write the equation of the line below in slope-intercept form.

Explanation:

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"current_concepts": [
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<reasoning>

Identify the y-intercept from the graph

\[
b = -7
\]

Determine the slope using two points on the line

\[

$$\begin{aligned} &\text{Points: } (0, -7) \text{ and } (3, -1)\\ &m = \frac{-1 - (-7)}{3 - 0} = \frac{6}{3} = 2 \end{aligned}$$

\]

Write the equation in slope-intercept form

\[

$$\begin{aligned} &y = mx + b\\ &y = 2x - 7 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 2x - 7\)
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, -7]],
"properties": {
"name": "(0, -7)",
"size": 3,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[3, -1]],
"properties": {
"name": "(3, -1)",
"size": 3,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "2*x - 7", "latex": "y = 2x - 7"}, -2, 8],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
]
}
</plot>

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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
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"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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"Slope-Intercept Form"
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"Slope of a Line",
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"Slope-Intercept Form"
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</pre_analysis>

<reasoning>

Identify the y-intercept from the graph

\[
b = -7
\]

Determine the slope using two points on the line

\[

$$\begin{aligned} &\text{Points: } (0, -7) \text{ and } (3, -1)\\ &m = \frac{-1 - (-7)}{3 - 0} = \frac{6}{3} = 2 \end{aligned}$$

\]

Write the equation in slope-intercept form

\[

$$\begin{aligned} &y = mx + b\\ &y = 2x - 7 \end{aligned}$$

\]
</reasoning>

<answer>
\(y = 2x - 7\)
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, -7]],
"properties": {
"name": "(0, -7)",
"size": 3,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[3, -1]],
"properties": {
"name": "(3, -1)",
"size": 3,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "2*x - 7", "latex": "y = 2x - 7"}, -2, 8],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
]
}
</plot>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
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