Answer
$$ y=-3x+5$$
Work Step by Step
Given $$f(x)=5-3 x, \quad a=2$$
Since $f(2)=-1$ and
$$ f^{\prime}(a) =\lim _{h \rightarrow 0} \frac{f(a+h)-f(a)}{h}$$
Then
\begin{aligned}
f^{\prime}(2) & =\lim _{h \rightarrow 0} \frac{5-3(2+h)-5+6}{h} \\
&=\lim _{h \rightarrow 0} \frac{ -3h}{h}\\
&=-3
\end{aligned}
Then the tangent line at $x=2$ is given by
\begin{align*}
\frac{y-y_1}{x-x_1}&=f'(a)\\
\frac{y+1}{x-2}&=-3\\
y+1&= -3x+6
\end{align*}
Hence $$ y=-3x+5$$
