The **slope of the curve** $y=f(x)$ at the point $P\left(x_{0}, f\left(x_{0}\right)\right)$ is the number $ m=\lim _{h \rightarrow 0} \frac{f\left(x_{0}+h\right)-f\left(x_{0}\right)}{h} \quad \text { (provided the limit exists). } $ The [[Tangent line]] to the curve at P is the line through P with this slope. This is the [[Limit (ε, δ)|limit]] of the [[Difference Quotient]], and will also be defined as the [[Derivative at a point]]