Find the equation of the tangent line and normal line

$\mathit{F}\mathit{i}\mathit{n}\mathit{d}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{e}\mathit{q}\mathit{u}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathbf{t}\mathbf{a}\mathbf{n}\mathit{g}\mathit{e}\mathit{n}\mathit{t}\mathbf{ }\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathbf{ }\mathit{a}\mathit{n}\mathit{d}\mathbf{ }\mathit{n}\mathit{o}\mathit{r}\mathit{m}\mathit{a}\mathit{l}\mathbf{ }\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathbf{ }$

$$\begin{gathered} \text{ \\ to the graph of y=4x+1 at 1, 2} \end{gathered}$$

$$\begin{gathered} \text{ \\ } \end{gathered}$$

$\mathit{S}\mathit{t}\mathit{e}\mathit{p}\mathbf{ }\mathbf{1}\mathbf{:}\mathbf{ }\mathit{U}\mathit{s}\mathit{e}\mathbf{ }\mathit{t}\mathit{h}\mathit{e}\mathbf{ }\mathit{d}\mathit{i}\mathit{f}\mathit{f}\mathit{e}\mathit{r}\mathit{e}\mathit{n}\mathit{t}\mathit{i}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathbf{ }\mathit{f}\mathit{o}\mathit{r}\mathit{m}\mathit{u}\mathit{l}\mathit{a}\mathbf{ }$

$$\begin{gathered} \text{ \\ ddxcu=-cu2ddxu } \end{gathered}$$

$$\begin{gathered} \text{ \\ y'=-4x+12 (1) \\ } \end{gathered}$$

$\mathit{:}\mathit{ }\mathit{A}\mathit{t}\mathit{ }\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t}\mathit{ }\mathit{(}\mathit{1}\mathit{,}\mathit{ }\mathit{2}\mathit{)}$

$$\begin{gathered} \text{ \\ dydx=-41+12 =-1 \\ } \end{gathered}$$

$\mathrm{Hence}, \mathrm{slope} \mathrm{of} \mathrm{the} \mathrm{tangent} \mathrm{line} \mathrm{at} (1, 2) \mathrm{equals} -1$

$\mathrm{while} \mathrm{slope} \mathrm{of} \mathrm{the} \mathrm{normal} \mathrm{line} \mathrm{at} \mathrm{the} \mathrm{point} \mathrm{is} 1.$

$\mathit{Step\; 2:\; U}\mathit{s}\mathit{i}\mathit{n}\mathit{g}\mathit{ }\mathit{t}\mathit{h}\mathit{e}\mathit{ }\mathit{p}\mathit{o}\mathit{i}\mathit{n}\mathit{t-}\mathit{s}\mathit{l}\mathit{o}\mathit{p}\mathit{e}\mathit{ }\mathit{f}\mathit{o}\mathit{r}\mathit{m}\mathit{ }\mathit{o}\mathit{f}\mathit{ }\mathit{t}\mathit{h}\mathit{e}\mathit{ }\mathit{e}\mathit{q}\mathit{u}\mathit{a}\mathit{t}\mathit{i}\mathit{o}\mathit{n}\mathit{ }\mathit{o}\mathit{f}\mathit{ }\mathit{t}\mathit{h}\mathit{e}\mathit{ }\mathit{l}\mathit{i}\mathit{n}\mathit{e}\mathit{.}$

$$\begin{gathered} \text{ \\ y-y1=m(x-x1) \\ } \end{gathered}$$

$\mathbf{E}\mathbf{q}\mathbf{u}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{t}\mathbf{a}\mathbf{n}\mathbf{g}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{ }\mathbf{l}\mathbf{i}\mathbf{n}\mathbf{e}\mathbf{:}$

$$\begin{gathered} \text{ \\ y-2=-1(x-1)} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-2=-x+1} \end{gathered}$$

$$\begin{gathered} \text{ \\ x+y-3=0 \\ } \end{gathered}$$

$\mathbf{E}\mathbf{q}\mathbf{u}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n}\mathbf{ }\mathbf{o}\mathbf{f}\mathbf{ }\mathbf{t}\mathbf{h}\mathbf{e}\mathbf{ }\mathbf{n}\mathbf{o}\mathbf{r}\mathbf{m}\mathbf{a}\mathbf{l}\mathbf{ }\mathbf{l}\mathbf{i}\mathbf{n}\mathbf{e}\mathbf{:}$

$$\begin{gathered} \text{ \\ y-2=1(x-1)} \end{gathered}$$

$$\begin{gathered} \text{ \\ y-x-1=0} \end{gathered}$$

$$\begin{gathered} \text{ \\ x-y+1=0 \\ } \end{gathered}$$