Question

total cost
9
8
7
(2, 7)
6
5
4
3
2
1
1 2 3 4 5 x
number of issues

\\(y = x + \frac{2}{7}\\)

\\(y = x + \frac{7}{2}\\)

\\(y = \frac{2}{7}x\\)

\\(y = \frac{7}{2}x\\)

Explanation:

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"concepts_used": [
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<reasoning>

Identify the key features of the graph

Using the Graphing Proportional Relationships knowledge point
The graph displays a straight line passing through the origin \((0,0)\), which represents a proportional relationship between the number of issues \(x\) and the total cost \(y\). We are given a specific point on this line: \((2, 7)\).

Calculate the constant of proportionality

Using the Constant of Proportionality knowledge point
\[
k = \frac{y}{x} = \frac{7}{2}
\]

Write the proportional equation

Using the Proportional Relationship Equation knowledge points
\[
y = kx \implies y = \frac{7}{2}x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = x + \frac{2}{7}\)</mcq-option>
<mcq-option>(B) \(y = x + \frac{7}{2}\)</mcq-option>
<mcq-option>(C) \(y = \frac{2}{7}x\)</mcq-option>
<mcq-correct>(D) \(y = \frac{7}{2}x\)</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Relationship Equation"
]
}
</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the key features of the graph

Using the Graphing Proportional Relationships knowledge point
The graph displays a straight line passing through the origin \((0,0)\), which represents a proportional relationship between the number of issues \(x\) and the total cost \(y\). We are given a specific point on this line: \((2, 7)\).

Calculate the constant of proportionality

Using the Constant of Proportionality knowledge point
\[
k = \frac{y}{x} = \frac{7}{2}
\]

Write the proportional equation

Using the Proportional Relationship Equation knowledge points
\[
y = kx \implies y = \frac{7}{2}x
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = x + \frac{2}{7}\)</mcq-option>
<mcq-option>(B) \(y = x + \frac{7}{2}\)</mcq-option>
<mcq-option>(C) \(y = \frac{2}{7}x\)</mcq-option>
<mcq-correct>(D) \(y = \frac{7}{2}x\)</mcq-correct>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Proportional Relationship Equation"
]
}
</post_analysis>