Question

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

\\m = -1\\

write the equation of this line in point-slope form using the point \\((4, 3)\\).

\\y - ? = \box (x - \box)\\

Explanation:

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"blank_filling_formatter",
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"needs_drawing": true,
"concepts_used": [
"Slope Calculation",
"Slope-Intercept Form"
],
"new_concepts": [
"Point-Slope Form"
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"Slope Calculation",
"Slope-Intercept Form",
"Point-Slope Form"
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</pre_analysis>

<reasoning>

Identify the point-slope formula

The point-slope form of a linear equation is:
\[y - y_1 = m(x - x_1)\]
where \(m\) is the slope and \((x_1, y_1)\) is a given point on the line.

Substitute the given values

Using the Slope Calculation and Slope-Intercept Form knowledge points
\[

$$\begin{aligned} &m = -1\\ &(x_1, y_1) = (4, 3)\\ &y - 3 = -1(x - 4) \end{aligned}$$

\]

Identify the missing value in the first box

The question asks for the value in the box containing the question mark:
\[y - [?] = \Box(x - \Box)\]
Comparing this to \(y - 3 = -1(x - 4)\), the value in the first box is \(3\).
</reasoning>

<answer>
A line intersects the points \((4, 3)\) and \((11, -4)\).
\(m = -1\)

Write the equation of this line in point-slope form using the point \((4, 3)\).

\(y -\) <blank>3</blank> \(= -1(x - 4)\)
</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
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Point-Slope Form"
]
}
</post_analysis>

Answer:

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"blank_filling_formatter",
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"needs_drawing": true,
"concepts_used": [
"Slope Calculation",
"Slope-Intercept Form"
],
"new_concepts": [
"Point-Slope Form"
],
"current_concepts": [
"Slope Calculation",
"Slope-Intercept Form",
"Point-Slope Form"
]
}
</pre_analysis>

<reasoning>

Identify the point-slope formula

The point-slope form of a linear equation is:
\[y - y_1 = m(x - x_1)\]
where \(m\) is the slope and \((x_1, y_1)\) is a given point on the line.

Substitute the given values

Using the Slope Calculation and Slope-Intercept Form knowledge points
\[

$$\begin{aligned} &m = -1\\ &(x_1, y_1) = (4, 3)\\ &y - 3 = -1(x - 4) \end{aligned}$$

\]

Identify the missing value in the first box

The question asks for the value in the box containing the question mark:
\[y - [?] = \Box(x - \Box)\]
Comparing this to \(y - 3 = -1(x - 4)\), the value in the first box is \(3\).
</reasoning>

<answer>
A line intersects the points \((4, 3)\) and \((11, -4)\).
\(m = -1\)

Write the equation of this line in point-slope form using the point \((4, 3)\).

\(y -\) <blank>3</blank> \(= -1(x - 4)\)
</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
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Point-Slope Form"
]
}
</post_analysis>