Question

graphing ax + by = c from intercepts

drag the red and blue dots along the x-axis and y-axis to graph
\\4x - 10y = 40.\\

Explanation:

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<reasoning>

Find the x-intercept

Using the x-intercept knowledge point
\[

$$\begin{aligned} &y = 0 \\ &4x - 10(0) = 40 \\ &4x = 40 \\ &x = 10 \end{aligned}$$

\]
The x-intercept is at \((10, 0)\).

Find the y-intercept

Using the y-intercept knowledge point
\[

$$\begin{aligned} &x = 0 \\ &4(0) - 10y = 40 \\ &-10y = 40 \\ &y = -4 \end{aligned}$$

\]
The y-intercept is at \((0, -4)\).

Graph the linear equation

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Plot } (10, 0) \text{ on the x-axis.} \\ &\text{Plot } (0, -4) \text{ on the y-axis.} \end{aligned}$$

\]
Draw the line passing through both points.
</reasoning>

<answer>
To graph the equation \(4x - 10y = 40\), drag the dots to the following coordinates:

• Red dot (on the x-axis): \((10, 0)\)
• Blue dot (on the y-axis): \((0, -4)\)

</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[10, 0]],
"properties": {
"name": "(10, 0)",
"size": 4,
"strokeColor": "#F2557F",
"fillColor": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, -4]],
"properties": {
"name": "(0, -4)",
"size": 4,
"strokeColor": "#5583F2",
"fillColor": "#5583F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[10, 0], [0, -4]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
],
"timestamps": [0.5, 1.0, 1.5]
}
</plot>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphing Linear Equations"
]
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</post_analysis>

Answer:

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<reasoning>

Find the x-intercept

Using the x-intercept knowledge point
\[

$$\begin{aligned} &y = 0 \\ &4x - 10(0) = 40 \\ &4x = 40 \\ &x = 10 \end{aligned}$$

\]
The x-intercept is at \((10, 0)\).

Find the y-intercept

Using the y-intercept knowledge point
\[

$$\begin{aligned} &x = 0 \\ &4(0) - 10y = 40 \\ &-10y = 40 \\ &y = -4 \end{aligned}$$

\]
The y-intercept is at \((0, -4)\).

Graph the linear equation

Using the Graphing Linear Equations knowledge point
\[

$$\begin{aligned} &\text{Plot } (10, 0) \text{ on the x-axis.} \\ &\text{Plot } (0, -4) \text{ on the y-axis.} \end{aligned}$$

\]
Draw the line passing through both points.
</reasoning>

<answer>
To graph the equation \(4x - 10y = 40\), drag the dots to the following coordinates:

• Red dot (on the x-axis): \((10, 0)\)
• Blue dot (on the y-axis): \((0, -4)\)

</answer>

<plot>
{
"elements": [
{
"type": "point",
"params": [[10, 0]],
"properties": {
"name": "(10, 0)",
"size": 4,
"strokeColor": "#F2557F",
"fillColor": "#F2557F",
"withLabel": true
}
},
{
"type": "point",
"params": [[0, -4]],
"properties": {
"name": "(0, -4)",
"size": 4,
"strokeColor": "#5583F2",
"fillColor": "#5583F2",
"withLabel": true
}
},
{
"type": "line",
"params": [[10, 0], [0, -4]],
"properties": {
"strokeColor": "#8C55F2",
"strokeWidth": 2
}
}
],
"timestamps": [0.5, 1.0, 1.5]
}
</plot>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Free Response",
"knowledge_point": [
"Mathematics",
"Algebra",
"Graphing Linear Equations"
]
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