Question

what is the point-slope form of a line that has a slope of \\(\frac{1}{2}\\) and passes through point \\((-7, 2)\\)?

\\(2 - y = \frac{1}{2}(7 - x)\\)

\\(7 - y = \frac{1}{2}(-2 - x)\\)

\\(y - 7 = \frac{1}{2}(x - 2)\\)

\\(y - 2 = \frac{1}{2}(x - (-7))\\)

Explanation:

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<reasoning>

Identify the point-slope formula

\[
y - y_1 = m(x - x_1)
\]

Substitute the given values

\[

$$\begin{aligned} &m = \frac{1}{2}\\ &(x_1, y_1) = (-7, 2)\\ &y - 2 = \frac{1}{2}(x - (-7)) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2-y=\frac{1}{2}(7-x)\)</mcq-option>
<mcq-option>(B) \(7-y=\frac{1}{2}(-2-x)\)</mcq-option>
<mcq-option>(C) \(y-7=\frac{1}{2}(x-2)\)</mcq-correct>
<mcq-correct>(D) \(y-2=\frac{1}{2}(x-(-7))\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Point-Slope Form"
]
}
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Answer:

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<reasoning>

Identify the point-slope formula

\[
y - y_1 = m(x - x_1)
\]

Substitute the given values

\[

$$\begin{aligned} &m = \frac{1}{2}\\ &(x_1, y_1) = (-7, 2)\\ &y - 2 = \frac{1}{2}(x - (-7)) \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) \(2-y=\frac{1}{2}(7-x)\)</mcq-option>
<mcq-option>(B) \(7-y=\frac{1}{2}(-2-x)\)</mcq-option>
<mcq-option>(C) \(y-7=\frac{1}{2}(x-2)\)</mcq-correct>
<mcq-correct>(D) \(y-2=\frac{1}{2}(x-(-7))\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Point-Slope Form"
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