# Curves

### Straight Line

- Cartesian equation:
- $y = mx + c$

- or parametrically:
- $x = at + b, y = ct +d$

### Description

The straight line must be one of the earliest curves studied, but Euclid in his*Elements*although he devotes much study to the straight line, does not consider it a curve.

In fact nobody attempted a general definition of a curve until Jordan in his

*Cours d'Analyse*in 1893.

The inverse of a straight line is a circle if the centre of inversion is not on the line.

The negative pedal of the straight line is a parabola if the pedal point is not on the line.

Since normals to a straight line never intersect and tangents coincide with the curve, evolutes, involutes and pedal curves are not too interesting.

**Other Web site:**

Jeff Miller (Why is the slope of a straight line called $m$?)