Solve the Problem $f ( x ) = \frac { 1 } { x }$

Multiple Choice

Solve the problem.
-Find equations of all tangents to the curve $f ( x ) = \frac { 1 } { x }$ that have slope $- 1$ .

A) $y = - x + 2 , y = - x - 2$
B) $y = x + 2 , y = x - 2$
C) $y = x - 2$
D) $y = - x + 2$