Question

a line intersects the points \\((4, 3)\\) and \\((11, -4)\\).

what is the slope of this line in simplest form?

\\(m = ? \\)

Explanation:

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<reasoning>

Identify the given coordinates

Using the Slope Calculation knowledge point
\[
(x_1, y_1) = (4, 3),\quad (x_2, y_2) = (11, -4)
\]

Calculate the slope

Using the Slope Calculation knowledge point
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 3}{11 - 4} = \frac{-7}{7} = -1
\]
</reasoning>

<answer>
A line intersects the points \((4, 3)\) and \((11, -4)\).

What is the slope of this line in simplest form?

\(m =\) <blank>-1</blank>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[4, 3]],
"properties": {
"name": "(4, 3)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[11, -4]],
"properties": {
"name": "(11, -4)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[4, 3], [11, -4]],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2
}
}
],
"timestamps": [0.5, 1.0]
}
</plot>

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"question_type": "Fill-in-the-blank",
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"Mathematics",
"Geometry",
"Slope Calculation"
]
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Answer:

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<reasoning>

Identify the given coordinates

Using the Slope Calculation knowledge point
\[
(x_1, y_1) = (4, 3),\quad (x_2, y_2) = (11, -4)
\]

Calculate the slope

Using the Slope Calculation knowledge point
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-4 - 3}{11 - 4} = \frac{-7}{7} = -1
\]
</reasoning>

<answer>
A line intersects the points \((4, 3)\) and \((11, -4)\).

What is the slope of this line in simplest form?

\(m =\) <blank>-1</blank>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[4, 3]],
"properties": {
"name": "(4, 3)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[11, -4]],
"properties": {
"name": "(11, -4)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[4, 3], [11, -4]],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2
}
}
],
"timestamps": [0.5, 1.0]
}
</plot>

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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
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"Geometry",
"Slope Calculation"
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