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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.

The word grade can sometimes be seen, but this is discouraged as it has a number of meanings.

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