Answer
$y=-\frac{1}{2}x+2$
Work Step by Step
Step 1. Given the function for the Witch of Agnesi as $y=\frac{8}{x^2+4}$, we can find the derivatives as $y'=\frac{-8(2x)}{(x^2+4)^2}=\frac{-16x}{(x^2+4)^2}$
Step 2. At the point $(2,1)$, the slope of the tangent is $m=\frac{-16(2)}{((2)^2+4)^2}=-\frac{1}{2}$
Step 3. The tangent line equation can be written as $y-1=-\frac{1}{2}(x-2)$ or $y=-\frac{1}{2}x+2$
