Question

question 11 (5 points)
select the graph of the equation \\(y + x + 3 = 0\\).

Explanation:

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<reasoning>

Rewrite the equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} y + x + 3 &= 0 \\ y &= -x - 3 \end{aligned}$$

\]

Identify slope and intercept

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} m &= -1 \\ b &= -3 \end{aligned}$$

\]

Find key graph points

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} (0, -3) \quad &\text{and} \quad (-3, 0) \end{aligned}$$

\]

Evaluate the options

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Option A: passes through } (0, -3) \text{ and } (-3, 0). \text{ Slope is } -1.\\ &\text{Option B: passes through } (0, -3) \text{ and } (-1, 0). \text{ Slope is } -3.\\ &\text{Option C: passes through } (0, 3) \text{ and } (-3, 0). \text{ Slope is } 1.\\ &\text{Option D: passes through } (0, -3) \text{ and } (-1, 0). \text{ Slope is } -3. \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) Line passing through (0, -3) and (-3, 0) with slope -1</mcq-correct>
<mcq-option>(B) Line passing through (0, -3) and (-1, 0) with slope -3</mcq-option>
<mcq-option>(C) Line passing through (0, 3) and (-3, 0) with slope 1</mcq-option>
<mcq-option>(D) Line passing through (0, -3) and (-1, 0) with slope -3</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "functiongraph",
"params": [
{
"js": "-x - 3",
"latex": "-x - 3"
},
-10,
10
],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"name": "y = -x - 3",
"withLabel": true
}
},
{
"type": "point",
"params": [
[0, -3]
],
"properties": {
"name": "(0, -3)",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [
[-3, 0]
],
"properties": {
"name": "(-3, 0)",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
}
],
"timestamps": [0.5, 1.0]
}
</plot>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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"new_concepts": [],
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</pre_analysis>

<reasoning>

Rewrite the equation

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} y + x + 3 &= 0 \\ y &= -x - 3 \end{aligned}$$

\]

Identify slope and intercept

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} m &= -1 \\ b &= -3 \end{aligned}$$

\]

Find key graph points

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} (0, -3) \quad &\text{and} \quad (-3, 0) \end{aligned}$$

\]

Evaluate the options

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Option A: passes through } (0, -3) \text{ and } (-3, 0). \text{ Slope is } -1.\\ &\text{Option B: passes through } (0, -3) \text{ and } (-1, 0). \text{ Slope is } -3.\\ &\text{Option C: passes through } (0, 3) \text{ and } (-3, 0). \text{ Slope is } 1.\\ &\text{Option D: passes through } (0, -3) \text{ and } (-1, 0). \text{ Slope is } -3. \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) Line passing through (0, -3) and (-3, 0) with slope -1</mcq-correct>
<mcq-option>(B) Line passing through (0, -3) and (-1, 0) with slope -3</mcq-option>
<mcq-option>(C) Line passing through (0, 3) and (-3, 0) with slope 1</mcq-option>
<mcq-option>(D) Line passing through (0, -3) and (-1, 0) with slope -3</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "functiongraph",
"params": [
{
"js": "-x - 3",
"latex": "-x - 3"
},
-10,
10
],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3,
"name": "y = -x - 3",
"withLabel": true
}
},
{
"type": "point",
"params": [
[0, -3]
],
"properties": {
"name": "(0, -3)",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [
[-3, 0]
],
"properties": {
"name": "(-3, 0)",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
}
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"timestamps": [0.5, 1.0]
}
</plot>

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"Mathematics",
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