# Parametric Equations ![[Pasted image 20240424134255.png|300]] A path like this one *fails the vertical line test* and typically wouldn’t be described as a function. > [!NOTE] **Parametrizations of Plane Curves** > > If $x$ and $y$ are given as functions > $x=f(t),y=g(t)$ > over an interval $I$ of $t$-values > ## Derivatives of Parametric Equations $\frac{dy}{dx} = \frac{\frac{dy}{dt}}{\frac{dx}{dt}}$