Answer
\[\begin{align}
& {{m}_{\tan }}=0 \\
& y=5 \\
\end{align}\]
Work Step by Step
\[\begin{align}
& f\left( x \right)=5;\text{ }P\left( 1,5 \right) \\
& \text{a}\text{. Using the definition }\left( \text{1} \right) \\
& {{m}_{\tan }}=\underset{x\to a}{\mathop{\lim }}\,\frac{f\left( x \right)-f\left( a \right)}{x-a} \\
& \text{Let }a=1 \\
& {{m}_{\tan }}=0 \\
& \\
& \text{b}\text{. The equation of the tangent line at}\left( 1,5 \right)\text{ is} \\
& y-f\left( a \right)={{m}_{\tan }}\left( x-a \right) \\
& y-5=0\left( x-1 \right) \\
& y=5 \\
& \\
& \text{c}\text{. Graph} \\
\end{align}\]
