# Definition:Slope

## Definition

### Straight Line

Let $\LL$ be a straight line embedded in a Cartesian plane.

The slope of $\LL$ is defined as the tangent of the angle that $\LL$ makes with the $x$-axis.

### Curve

Let $P$ be a point on a curve $\CC$ embedded in a Cartesian plane.

The slope of $\CC$ at $P$ is defined as the slope of the tangent to $\CC$ at $P$.

## Also known as

The slope of a straight line or curve is also sometimes referred to as its gradient.

However, that term has a more generic and abstract meaning than does the concept of slope as given here.

Some sources suggest that the slope of a straight line is the same as its direction, but this is true only in the plane.