# Transcendental Slope

## Theorem

The slope of a line may be transcendental.

## Proof

The slope form of any number $x$ may be produced by:

 $\ds {\mathrm m}$ $=$ $\ds \frac {x} {1}$ (Slope Form of $x$)
 $\ds {\mathrm m}$ $=$ $\ds {x}$

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

 $\ds {\mathrm m}$ $=$ $\ds \frac {\mathrm \pi} {1}$ (Slope Form of $\pi$)
 $\ds {\mathrm m}$ $=$ $\ds {\mathrm \pi}$

Slope $m$ is transcendental.