Theorem
The slope of a line may be transcendental.
Proof
The slope form of any number $x$ may be produced by:
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\(\ds {\mathrm m}\)
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\(=\)
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\(\ds \frac {x} {1}\)
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(Slope Form of $x$)
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\(\ds {\mathrm m}\)
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\(=\)
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\(\ds {x}\)
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If $x$ is transcendental, then the slope of a line $\mathrm m$ is transcendental.
Example
$\mathrm \pi$ is proven to be transcendental by the Lindemann-Weiersrass Theorem
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\(\ds {\mathrm m}\)
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\(=\)
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\(\ds \frac {\mathrm \pi} {1}\)
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(Slope Form of $\pi$)
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\(\ds {\mathrm m}\)
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\(=\)
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\(\ds {\mathrm \pi}\)
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Slope $m$ is transcendental.