Answer
$f(x)=-x-2$
Work Step by Step
Using $y=mx+b$ or Slope-Intercept Form, the equation of the line with slope $
-1
$ and $y-$intercept $(
0,-2
)$ is
\begin{array}{l}
y=-x-2
.\end{array}
In function notation, this is equivalent to
\begin{array}{l}
f(x)=-x-2
.\end{array}