Question

which graph matches this direct variation equation?
\\y = -4x\\

Explanation:

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<reasoning>

Identify the slope and y-intercept

\[

$$\begin{aligned} &y = -4x \\ &\text{Slope } (m) = -4 \\ &\text{y-intercept } (b) = 0 \end{aligned}$$

\]

Determine key points on the graph

\[

$$\begin{aligned} &(x, y) = (0, 0) \\ &(x, y) = (-1, 4) \\ &(x, y) = (1, -4) \end{aligned}$$

\]

Match with the given graph options

\[

$$\begin{aligned} &\text{Graph 1 (Left): Passes through } (0,0) \text{ and } (4, -1) \implies m = -\frac{1}{4} \\ &\text{Graph 2 (Middle): Passes through } (0,0) \text{ and } (-1, 4) \implies m = -4 \\ &\text{Graph 3 (Right): Passes through } (0,0) \text{ and } (1, 4) \implies m = 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Left graph (slope of \(-\frac{1}{4}\))</mcq-option>
<mcq-correct>(B) Middle graph (slope of \(-4\))</mcq-correct>
<mcq-option>(C) Right graph (slope of \(4\))</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 0]],
"properties": {
"name": "O",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[-1, 4]],
"properties": {
"name": "A",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "-4*x", "latex": "y = -4x"}, -3, 3],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
}
]
}
</plot>

<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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<reasoning>

Identify the slope and y-intercept

\[

$$\begin{aligned} &y = -4x \\ &\text{Slope } (m) = -4 \\ &\text{y-intercept } (b) = 0 \end{aligned}$$

\]

Determine key points on the graph

\[

$$\begin{aligned} &(x, y) = (0, 0) \\ &(x, y) = (-1, 4) \\ &(x, y) = (1, -4) \end{aligned}$$

\]

Match with the given graph options

\[

$$\begin{aligned} &\text{Graph 1 (Left): Passes through } (0,0) \text{ and } (4, -1) \implies m = -\frac{1}{4} \\ &\text{Graph 2 (Middle): Passes through } (0,0) \text{ and } (-1, 4) \implies m = -4 \\ &\text{Graph 3 (Right): Passes through } (0,0) \text{ and } (1, 4) \implies m = 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) Left graph (slope of \(-\frac{1}{4}\))</mcq-option>
<mcq-correct>(B) Middle graph (slope of \(-4\))</mcq-correct>
<mcq-option>(C) Right graph (slope of \(4\))</mcq-option>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[0, 0]],
"properties": {
"name": "O",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[-1, 4]],
"properties": {
"name": "A",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "-4*x", "latex": "y = -4x"}, -3, 3],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 3
}
}
]
}
</plot>

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{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Direct Variation"
]
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