#### Answer

\[y = x + 1\]

#### Work Step by Step

\[\begin{gathered}
y = {e^x} \hfill \\
Evaluate\,\,the\,\,function\,\,at\,\,x = 0 \hfill \\
y\,\left( 0 \right) = {e^0} \hfill \\
y\,\left( 0 \right) = 1 \hfill \\
P\,oint\,\,\,\left( {0,1} \right) \hfill \\
Find\,\,the\,\,deriva\,tive\,\,of\,\,the\,\,function \hfill \\
{y^,} = \,\,{\left[ {{e^x}} \right]^,} \hfill \\
{y^,} = {e^x} \hfill \\
Evaluate\,\,{y^,}\,\,at\,\,x = 0 \hfill \\
m = {y^,}\,\left( 0 \right) = {e^0} = 1 \hfill \\
m = 1 \hfill \\
Use\,\,the\,\,point\, - slope\,\,form \hfill \\
y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\
y - 1 = 1\,\left( {x - 0} \right) \hfill \\
y = x + 1 \hfill \\
\end{gathered} \]