Question

question 8 (1 point)

which graph matches the equation \\(y = -3/4x + 2\\)?

Explanation:

<pre_analysis>
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"step_cot",
"multiple_choice_formatter",
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"quick"
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"concepts_used": [
"Slope-Intercept Form"
],
"new_concepts": [],
"current_concepts": [
"Slope-Intercept Form",
"Graphing Linear Equations"
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</pre_analysis>

<reasoning>

Identify the y-intercept and slope

\[

$$\begin{aligned} &y = -\frac{3}{4}x + 2 \\ &\text{y-intercept: } (0, 2) \\ &\text{slope } (m): -\frac{3}{4} \end{aligned}$$

\]

Find a second point on the line

\[

$$\begin{aligned} &x = 4 \\ &y = -\frac{3}{4}(4) + 2 = -3 + 2 = -1 \\ &\text{Point: } (4, -1) \end{aligned}$$

\]

Match with the correct graph

\[

$$\begin{aligned} &\text{Graph 1: Passes through } (0, 2) \text{ and } (4, 5) \implies m = \frac{3}{4} \\ &\text{Graph 2: Horizontal line } y = 2 \implies m = 0 \\ &\text{Graph 3: Passes through } (0, 2) \text{ and } (4, -1) \implies m = -\frac{3}{4} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Graph with a positive slope passing through (0, 2) and (4, 5)</mcq-option>
<mcq-option>(B) Graph of a horizontal line at y = 2</mcq-option>
<mcq-correct>(C) Graph with a negative slope passing through (0, 2) and (4, -1)</mcq-correct>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 2]],
"properties": {
"name": "(0, 2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[4, -1]],
"properties": {
"name": "(4, -1)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[0, 2], [4, -1]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
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],
"needs_drawing": true,
"concepts_used": [
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],
"new_concepts": [],
"current_concepts": [
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}
</pre_analysis>

<reasoning>

Identify the y-intercept and slope

\[

$$\begin{aligned} &y = -\frac{3}{4}x + 2 \\ &\text{y-intercept: } (0, 2) \\ &\text{slope } (m): -\frac{3}{4} \end{aligned}$$

\]

Find a second point on the line

\[

$$\begin{aligned} &x = 4 \\ &y = -\frac{3}{4}(4) + 2 = -3 + 2 = -1 \\ &\text{Point: } (4, -1) \end{aligned}$$

\]

Match with the correct graph

\[

$$\begin{aligned} &\text{Graph 1: Passes through } (0, 2) \text{ and } (4, 5) \implies m = \frac{3}{4} \\ &\text{Graph 2: Horizontal line } y = 2 \implies m = 0 \\ &\text{Graph 3: Passes through } (0, 2) \text{ and } (4, -1) \implies m = -\frac{3}{4} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Graph with a positive slope passing through (0, 2) and (4, 5)</mcq-option>
<mcq-option>(B) Graph of a horizontal line at y = 2</mcq-option>
<mcq-correct>(C) Graph with a negative slope passing through (0, 2) and (4, -1)</mcq-correct>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 2]],
"properties": {
"name": "(0, 2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[4, -1]],
"properties": {
"name": "(4, -1)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[0, 2], [4, -1]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
}
]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>