Step 1 :Find the derivative of the curve y=\(\frac{1}{x}\), which represents the slope of the tangent at any point on the curve.
Step 2 :The derivative of y=\(\frac{1}{x}\) is y'=\(-\frac{1}{x^2}\).
Step 3 :Substitute the x-coordinate of point P, -2, into the derivative to find the slope of the tangent at P: \(m = -\frac{1}{(-2)^2} = -\frac{1}{4}\).
Step 4 :\(\boxed{-\frac{1}{4}}\) is the slope of the tangent to the curve y=\(\frac{1}{x}\) at the point P\(\left(-2,-\frac{1}{2}\right)\).