Question

find the slope of the line.

\\3x + 2y = -1\\

write your answer in simplest form.

Explanation:

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<reasoning>

Rewrite the equation in slope-intercept form

\[

$$\begin{aligned} 3x + 2y &= -1 \\ 2y &= -3x - 1 \\ y &= -\frac{3}{2}x - \frac{1}{2} \end{aligned}$$

\]

Identify the slope from the equation

\[

$$\begin{aligned} y &= mx + b \\ m &= -\frac{3}{2} \end{aligned}$$

\]
</reasoning>

<answer>
Find the slope of the line.

\(3x + 2y = -1\)

Write your answer in simplest form.

<blank>\(-\frac{3}{2}\)</blank>
</answer>

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

Answer:

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<reasoning>

Rewrite the equation in slope-intercept form

\[

$$\begin{aligned} 3x + 2y &= -1 \\ 2y &= -3x - 1 \\ y &= -\frac{3}{2}x - \frac{1}{2} \end{aligned}$$

\]

Identify the slope from the equation

\[

$$\begin{aligned} y &= mx + b \\ m &= -\frac{3}{2} \end{aligned}$$

\]
</reasoning>

<answer>
Find the slope of the line.

\(3x + 2y = -1\)

Write your answer in simplest form.

<blank>\(-\frac{3}{2}\)</blank>
</answer>

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