Question

step 4: sketch the graph 1. draw a coordinate plane. 2. plot the points \\((4, 0)\\) and \\((0, -2)\\). 3. draw a straight line passing through both points.

Explanation:

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<reasoning>

Identify the given equation

Using the Slope-Intercept Form knowledge point
\[
2x - 4y = 8
\]

Solve for y in terms of x

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} -4y &= -2x + 8 \\ y &= \frac{-2}{-4}x + \frac{8}{-4} \\ y &= \frac{1}{2}x - 2 \end{aligned}$$

\]

Verify with the graph parameters

We check the slope \(m\) and y-intercept \(b\) from the graph:

• Slope \(m = \frac{1}{2}\)
• y-intercept \((0, -2)\)
• x-intercept \((4, 0)\)

These match the derived equation:
\[
y = \frac{1}{2}x - 2
\]
</reasoning>

<answer>
Line: \(y =\) <blank>\(\frac{1}{2}x - 2\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[4, 0]],
"properties": {
"name": "(4, 0)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, -2]],
"properties": {
"name": "(0, -2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "0.5*x - 2", "latex": "\frac{1}{2}x - 2"}, -3, 9],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 3
}
}
],
"timestamps": [0.5, 1.0, 1.5]
}
</plot>

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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Slope-Intercept Form"
]
}
</post_analysis>

Answer:

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<reasoning>

Identify the given equation

Using the Slope-Intercept Form knowledge point
\[
2x - 4y = 8
\]

Solve for y in terms of x

Using the Slope-Intercept Form knowledge point
\[

$$\begin{aligned} -4y &= -2x + 8 \\ y &= \frac{-2}{-4}x + \frac{8}{-4} \\ y &= \frac{1}{2}x - 2 \end{aligned}$$

\]

Verify with the graph parameters

We check the slope \(m\) and y-intercept \(b\) from the graph:

• Slope \(m = \frac{1}{2}\)
• y-intercept \((0, -2)\)
• x-intercept \((4, 0)\)

These match the derived equation:
\[
y = \frac{1}{2}x - 2
\]
</reasoning>

<answer>
Line: \(y =\) <blank>\(\frac{1}{2}x - 2\)</blank>
</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[4, 0]],
"properties": {
"name": "(4, 0)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, -2]],
"properties": {
"name": "(0, -2)",
"size": 4,
"color": "#8C55F2",
"withLabel": true
}
},
{
"type": "functiongraph",
"params": [{"js": "0.5*x - 2", "latex": "\frac{1}{2}x - 2"}, -3, 9],
"properties": {
"strokeColor": "#5583F2",
"strokeWidth": 3
}
}
],
"timestamps": [0.5, 1.0, 1.5]
}
</plot>

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"Mathematics",
"Algebra",
"Slope-Intercept Form"
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