Question

which graph matches this direct variation equation?
\\y = -\frac{3}{4}x\\

Explanation:

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"concepts_used": [
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"Slope-Intercept Form",
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<reasoning>

Identify the y-intercept of the direct variation equation

\[
y = -\frac{3}{4}x \implies \text{y-intercept} = (0,0)
\]

Determine the slope and a second point on the line

\[

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

\]

Match with the given graphs

\[

$$\begin{aligned} &\text{Graph 1: Passes through } (0, 2) \quad (\text{Incorrect}) \\ &\text{Graph 2: Passes through } (0, 0) \text{ and } (4, -3) \quad (\text{Correct}) \\ &\text{Graph 3: Passes through } (0, 0) \text{ and } (4, 3) \quad (\text{Incorrect}) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Graph 1: Line passing through (0, 2) and (4, -1)</mcq-option>
<mcq-correct>(B) Graph 2: Line passing through (0, 0) and (4, -3)</mcq-correct>
<mcq-option>(C) Graph 3: Line passing through (0, 0) and (4, 3)</mcq-option>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Direct Variation"
]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the y-intercept of the direct variation equation

\[
y = -\frac{3}{4}x \implies \text{y-intercept} = (0,0)
\]

Determine the slope and a second point on the line

\[

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

\]

Match with the given graphs

\[

$$\begin{aligned} &\text{Graph 1: Passes through } (0, 2) \quad (\text{Incorrect}) \\ &\text{Graph 2: Passes through } (0, 0) \text{ and } (4, -3) \quad (\text{Correct}) \\ &\text{Graph 3: Passes through } (0, 0) \text{ and } (4, 3) \quad (\text{Incorrect}) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Graph 1: Line passing through (0, 2) and (4, -1)</mcq-option>
<mcq-correct>(B) Graph 2: Line passing through (0, 0) and (4, -3)</mcq-correct>
<mcq-option>(C) Graph 3: Line passing through (0, 0) and (4, 3)</mcq-option>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Direct Variation"
]
}
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