Find the slope of the following curve at \( x=8 \) \( y=\frac{1}{x-4} \) The slope of the given curve at \( x=8 \) is (Simplify your answer.)

1. Given the function \[ y = \frac{1}{x-4}, \] we rewrite it as \[ y = (x-4)^{-1}. \] 2. Differentiate \( y \) with respect to \( x \) using the power rule: \[ \frac{dy}{dx} = -1 \cdot (x-4)^{-2} \cdot \frac{d}{dx}(x-4). \] Since \(\frac{d}{dx}(x-4)=1\), we have \[ \frac{dy}{dx} = -\frac{1}{(x-4)^2}. \] 3. Evaluate the derivative at \( x=8 \): \[ \frac{dy}{dx}\Big|_{x=8} = -\frac{1}{(8-4)^2} = -\frac{1}{4^2} = -\frac{1}{16}. \] The slope of the given curve at \( x=8 \) is \[ -\frac{1}{16}. \]