Question

drag the red and blue dots along the x-axis and y-axis to graph \\(-2x + y = 10\\)

Explanation:

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"needs_drawing": true,
"concepts_used": [
"x-intercept",
"y-intercept",
"Graphing Linear Equations"
],
"new_concepts": [],
"current_concepts": [
"x-intercept",
"y-intercept",
"Graphing Linear Equations"
]
}
</pre_analysis>

<reasoning>

Find the x-intercept

\[

$$\begin{aligned} -2x + (0) &= 10 \\ -2x &= 10 \\ x &= -5 \end{aligned}$$

\]

Find the y-intercept

\[

$$\begin{aligned} -2(0) + y &= 10 \\ y &= 10 \end{aligned}$$

\]

Identify the coordinates for the dots

\[

$$\begin{aligned} \text{Red dot (x-axis)}: & \ (-5, 0) \\ \text{Blue dot (y-axis)}: & \ (0, 10) \end{aligned}$$

\]
</reasoning>

<answer>

• Red dot (on the x-axis): Move to \((-5, 0)\)
• Blue dot (on the y-axis): Move to \((0, 10)\)

</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[-5, 0]],
"properties": {
"name": "Red Dot",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, 10]],
"properties": {
"name": "Blue Dot",
"size": 4,
"color": "#5583F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[-5, 0], [0, 10]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
]
}
</plot>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphing Linear Equations"
]
}
</post_analysis>

Answer:

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],
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"concepts_used": [
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"Graphing Linear Equations"
],
"new_concepts": [],
"current_concepts": [
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"Graphing Linear Equations"
]
}
</pre_analysis>

<reasoning>

Find the x-intercept

\[

$$\begin{aligned} -2x + (0) &= 10 \\ -2x &= 10 \\ x &= -5 \end{aligned}$$

\]

Find the y-intercept

\[

$$\begin{aligned} -2(0) + y &= 10 \\ y &= 10 \end{aligned}$$

\]

Identify the coordinates for the dots

\[

$$\begin{aligned} \text{Red dot (x-axis)}: & \ (-5, 0) \\ \text{Blue dot (y-axis)}: & \ (0, 10) \end{aligned}$$

\]
</reasoning>

<answer>

• Red dot (on the x-axis): Move to \((-5, 0)\)
• Blue dot (on the y-axis): Move to \((0, 10)\)

</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[-5, 0]],
"properties": {
"name": "Red Dot",
"size": 4,
"color": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, 10]],
"properties": {
"name": "Blue Dot",
"size": 4,
"color": "#5583F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[-5, 0], [0, 10]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphing Linear Equations"
]
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