Question

the point-slope form of a line that has a slope of \\(\frac{2}{3}\\) and passes through point \\((6, 0)\\) is shown below.

\\y - 0 = \frac{2}{3}(x - 6)\\

what is the equation in slope-intercept form?

\\(y = \frac{2}{3}x - 12\\)
\\(y = \frac{2}{3}x - 6\\)
\\(y = \frac{2}{3}x - 4\\)
\\(y = \frac{2}{3}x - 8\\)

Explanation:

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<reasoning>

Distribute the slope on the right side

\[
y - 0 = \frac{2}{3}(x - 6)
\]
\[
y - 0 = \frac{2}{3}x - \frac{2}{3}(6)
\]

Simplify the constant term

\[
\frac{2}{3}(6) = 4
\]
\[
y = \frac{2}{3}x - 4
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = \frac{2}{3}x - 12\)</mcq-option>
<mcq-option>(B) \(y = \frac{2}{3}x - 6\)</mcq-option>
<mcq-correct>(C) \(y = \frac{2}{3}x - 4\)</mcq-correct>
<mcq-option>(D) \(y = \frac{2}{3}x - 8\)</mcq-option>
</answer>

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Answer:

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<reasoning>

Distribute the slope on the right side

\[
y - 0 = \frac{2}{3}(x - 6)
\]
\[
y - 0 = \frac{2}{3}x - \frac{2}{3}(6)
\]

Simplify the constant term

\[
\frac{2}{3}(6) = 4
\]
\[
y = \frac{2}{3}x - 4
\]
</reasoning>

<answer>
<mcq-option>(A) \(y = \frac{2}{3}x - 12\)</mcq-option>
<mcq-option>(B) \(y = \frac{2}{3}x - 6\)</mcq-option>
<mcq-correct>(C) \(y = \frac{2}{3}x - 4\)</mcq-correct>
<mcq-option>(D) \(y = \frac{2}{3}x - 8\)</mcq-option>
</answer>

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"question_type": "Multiple Choice",
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