Answer
\[y = - 2x - 4\]
Work Step by Step
\[\begin{gathered}
y = {x^2} - 6x\,\,\,,\,\,\,x = 2 \hfill \\
Evaluate\,\,the\,\,function\,\,at\,\,x = 2 \hfill \\
y\,\left( 2 \right) = \,{\left( 2 \right)^2} - 6\,\left( 2 \right) \hfill \\
y\,\left( 2 \right) = - 8 \hfill \\
Point\,\,\,\left( {2, - 8} \right) \hfill \\
Find\,\,the\,\,derivative\,\,of\,\,the\,\,fuction \hfill \\
{y^,} = \,{\left( {{x^2} - 6x} \right)^,} \hfill \\
{y^,} = 2x - 6 \hfill \\
m = {y^,}\,\left( 2 \right) = 2\,\left( 2 \right) - 6 \hfill \\
m = - 2 \hfill \\
Point - slope\,\,form\,\, \hfill \\
y - {y_1} = m\,\left( {x - {x_1}} \right) \hfill \\
y - \,\left( { - 8} \right) = - 2\,\left( {x - 2} \right) \hfill \\
Simplifying \hfill \\
y + 8 = - 2\,\left( {x - 2} \right) \hfill \\
y + 8 = - 2x + 4 \hfill \\
y = - 2x - 4 \hfill \\
\end{gathered} \]
