# Definition:Slope

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## 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.

## Sources

- 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**slope**