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Home » So the largest integer $k$ is $14$. - Upplift

So the largest integer $k$ is $14$. - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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🔥 Popular Posts

Given line: \( 3x - 4y + 12 = 0 \), and point \( P = (1, 2) \).
The slope of the line: rewrite in slope-intercept form:
3x + 12 = 4y \Rightarrow y = \frac{3}{4}x + 3
So slope \( m = \frac{3}{4} \). The perpendicular slope is \( -\frac{4...
The line through \( (1, 2) \) with slope \( -\frac{4}{3} \) is:
y - 2 = -\frac{4}{3}(x - 1)
\Rightarrow y = -\frac{4}{3}x + \frac{4}{3} + 2 = -\frac{4}{3}x + \fra...
Now find intersection with original line \( 3x - 4y + 12 = 0 \).
Substitute \( y = -\frac{4}{3}x + \frac{10}{3} \):
3x - 4\left(-\frac{4}{3}x + \frac{10}{3}\right) + 12 = 0

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