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

We are given the linear equation shown on the graph:
\[2x - 4y = 8\]

Solve for y in terms of x

To find the slope-intercept form \(y = mx + b\), we isolate \(y\):
\[-4y = -2x + 8\]
Divide both sides by \(-4\):
\[y = \frac{-2}{-4}x + \frac{8}{-4}\]
\[y = \frac{1}{2}x - 2\]

Verify with graph features

The equation \(y = \frac{1}{2}x - 2\) has:

• A \(y\)-intercept at \((0, -2)\).
• An \(x\)-intercept at \((4, 0)\).
• A slope of \(m = \frac{1}{2}\).

These values perfectly match the plotted line and labels in the image.
</reasoning>

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

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

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

Answer:

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<reasoning>

Identify the given equation

We are given the linear equation shown on the graph:
\[2x - 4y = 8\]

Solve for y in terms of x

To find the slope-intercept form \(y = mx + b\), we isolate \(y\):
\[-4y = -2x + 8\]
Divide both sides by \(-4\):
\[y = \frac{-2}{-4}x + \frac{8}{-4}\]
\[y = \frac{1}{2}x - 2\]

Verify with graph features

The equation \(y = \frac{1}{2}x - 2\) has:

• A \(y\)-intercept at \((0, -2)\).
• An \(x\)-intercept at \((4, 0)\).
• A slope of \(m = \frac{1}{2}\).

These values perfectly match the plotted line and labels in the image.
</reasoning>

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

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

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