Answer
\[s\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{1\,\,\,\,\,\,\,\,{\text{if}}\,\,\,x\, < 0} \\
{ - \frac{1}{2}\,\,\,\,{\text{if}}\,\,\,\,x > 0}
\end{array}} \right.\]
Work Step by Step
$$\eqalign{
& {\text{Calculate the slope for the intervals }}x < 0{\text{ and }}x > 0 \cr
& \cr
& {\text{For }}x < 0{\text{ we can use the points }}\left( { - 3,0} \right){\text{ and }}\left( {0,3} \right), \cr
& {\text{then}} \cr
& m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{3 - 0}}{{0 - \left( { - 3} \right)}} \cr
& m = \frac{3}{3} = 1 \cr
& \cr
& {\text{For }}x > 0{\text{ we can use the points }}\left( {0,3} \right){\text{ and }}\left( {2,2} \right), \cr
& m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{2 - 3}}{{2 - 0}} \cr
& m = - \frac{1}{2} \cr
& \cr
& {\text{Therefore,}} \cr} $$
\[s\left( x \right) = \left\{ {\begin{array}{*{20}{c}}
{1\,\,\,\,\,\,\,\,{\text{if}}\,\,\,x\, < 0} \\
{ - \frac{1}{2}\,\,\,\,{\text{if}}\,\,\,\,x > 0}
\end{array}} \right.\]
