Answer
\[y = - 2x + 9\]
Work Step by Step
\[\begin{gathered}
y = 8 - {x^2}\,\,,\,\,x = 1 \hfill \\
Evaluate\,\,the\,\,function\,\,at\,\,x = 1 \hfill \\
y\,\left( 1 \right) = 8 - \,{\left( 1 \right)^2} \hfill \\
y\,\left( 1 \right) = 7 \hfill \\
Point\,\,\,\left( {1,7} \right) \hfill \\
Find\,\,the\,\,derivative\,\,of\,\,the\,\,fuction \hfill \\
{y^,} = \,{\left( {8 - {x^2}} \right)^,} \hfill \\
{y^,} = - 2x \hfill \\
m = {y^,}\,\left( 1 \right) = - 2\,\left( 1 \right) \hfill \\
m = - 2 \hfill \\
Point - slope\,\,form\,\, \hfill \\
y - 7 = - 2\,\left( {x - 1} \right) \hfill \\
Simplifying \hfill \\
y - 7 = - 2x + 2 \hfill \\
y = - 2x + 9 \hfill \\
\end{gathered} \]
