Question

find the slope of the line that passes through

1. \\((0,2)\\) and \\((4,6)\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Slope Formula"
],
"current_concepts": [
"Slope Formula",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Identify the given coordinates

\[
(x_1, y_1) = (0, 2),\quad (x_2, y_2) = (4, 6)
\]

Apply the slope formula

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Calculate the slope value

\[
m = \frac{6 - 2}{4 - 0} = \frac{4}{4} = 1
\]
</reasoning>

<answer>
\(1\)
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 2]],
"properties": {
"name": "(0,2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[4, 6]],
"properties": {
"name": "(4,6)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[0, 2], [4, 6]],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope Formula"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"explain_then_answer",
"quick"
],
"needs_drawing": true,
"concepts_used": [],
"new_concepts": [
"Slope Formula"
],
"current_concepts": [
"Slope Formula",
"Linear Equations"
]
}
</pre_analysis>

<reasoning>

Identify the given coordinates

\[
(x_1, y_1) = (0, 2),\quad (x_2, y_2) = (4, 6)
\]

Apply the slope formula

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Calculate the slope value

\[
m = \frac{6 - 2}{4 - 0} = \frac{4}{4} = 1
\]
</reasoning>

<answer>
\(1\)
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 2]],
"properties": {
"name": "(0,2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[4, 6]],
"properties": {
"name": "(4,6)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[0, 2], [4, 6]],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 2
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope Formula"
]
}
</post_analysis>