Find \( \frac{d y}{d x} \) by implicit differentiation. Then find the slope of the graph at the given point. (If an answer is undefined, enter UNDEFINED.) \[ \frac{d y}{d x}=\text { undefined } \] At \( (-6,-5): y^{\prime}=-\frac{5}{6}, \quad(-6,-5) \)

To find \( \frac{d y}{d x} \) by implicit differentiation, we need to start with the equation that relates \( x \) and \( y \). However, it seems that the equation is not provided in your message. Let's assume we have an implicit function \( F(x, y) = 0 \). The process of implicit differentiation involves differentiating both sides of the equation with respect to \( x \) and applying the chain rule to terms involving \( y \). Here are the steps to find \( \frac{d y}{d x} \): 1. Differentiate both sides of the equation \( F(x, y) = 0 \) with respect to \( x \): \[ \frac{d}{dx} F(x, y) = \frac{\partial F}{\partial x} + \frac{\partial F}{\partial y} \frac{d y}{d x} = 0 \] 2. Solve for \( \frac{d y}{d x} \): \[ \frac{\partial F}{\partial y} \frac{d y}{d x} = -\frac{\partial F}{\partial x} \] \[ \frac{d y}{d x} = -\frac{\frac{\partial F}{\partial x}}{\frac{\partial F}{\partial y}} \] 3. Substitute the values of \( x \) and \( y \) at the given point to find the slope. Since you mentioned that at the point \( (-6, -5) \), \( y' = -\frac{5}{6} \), we can conclude that the slope of the graph at that point is \( -\frac{5}{6} \). If you have a specific equation in mind, please provide it, and I can perform the implicit differentiation step-by-step for that equation.