Question

what inequality is shown in the graph?

Explanation:

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<reasoning>

Find the boundary line equation

The boundary line is dashed, passing through the y-intercept \((0, 1)\) and the x-intercept \((-0.33, 0)\), or more clearly through points \((0, 1)\) and \((-1, -2)\).
\[
\text{Slope } m = \frac{-2 - 1}{-1 - 0} = \frac{-3}{-1} = 3
\]
\[
\text{Equation: } y = 3x + 1
\]

Determine the inequality sign

The boundary line is dashed, so the inequality is strict (\(<\) or \(>\)).
The shaded region is to the left/above the line. Testing the point \((-2, 0)\):
\[
0 > 3(-2) + 1 \implies 0 > -5 \quad (\text{True})
\]
Thus, the inequality is:
\[
y > 3x + 1
\]
</reasoning>

<answer>
What inequality is shown in the graph? <blank>\(y > 3x + 1\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "inequality",
"params": [
{
"js": "3*x + 1",
"latex": "3x + 1"
},
[-2, 2]
],
"properties": {
"inverse": true,
"strict": true,
"strokeColor": "#8C55F2",
"fillColor": "rgba(140, 85, 242, 0.3)",
"strokeWidth": 2,
"dash": 2
}
}
],
"timestamps": [0.5]
}
</plot>

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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphing Linear Inequalities"
]
}
</post_analysis>

Answer:

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<reasoning>

Find the boundary line equation

The boundary line is dashed, passing through the y-intercept \((0, 1)\) and the x-intercept \((-0.33, 0)\), or more clearly through points \((0, 1)\) and \((-1, -2)\).
\[
\text{Slope } m = \frac{-2 - 1}{-1 - 0} = \frac{-3}{-1} = 3
\]
\[
\text{Equation: } y = 3x + 1
\]

Determine the inequality sign

The boundary line is dashed, so the inequality is strict (\(<\) or \(>\)).
The shaded region is to the left/above the line. Testing the point \((-2, 0)\):
\[
0 > 3(-2) + 1 \implies 0 > -5 \quad (\text{True})
\]
Thus, the inequality is:
\[
y > 3x + 1
\]
</reasoning>

<answer>
What inequality is shown in the graph? <blank>\(y > 3x + 1\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "inequality",
"params": [
{
"js": "3*x + 1",
"latex": "3x + 1"
},
[-2, 2]
],
"properties": {
"inverse": true,
"strict": true,
"strokeColor": "#8C55F2",
"fillColor": "rgba(140, 85, 242, 0.3)",
"strokeWidth": 2,
"dash": 2
}
}
],
"timestamps": [0.5]
}
</plot>

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"Algebra",
"Graphing Linear Inequalities"
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