Answer
The graph is shown below:
Work Step by Step
We have to find any two solutions of the linear equation, plot the graph of the linear equation
$ y={{3}^{x-2}}$
To find the value of the y-intercept, substitute $ x=0$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{0-2}} \\
& y={{3}^{-2}} \\
& x=\frac{1}{{{3}^{2}}}
\end{align}$
$ x=\frac{1}{9}$
To find the value of the y-intercept, substitute $ x=1$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{1-2}} \\
& y={{3}^{-1}} \\
& y=\frac{1}{3}
\end{align}$
To find the value of the y-intercept, substitute $ x=2$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{2-2}} \\
& y={{3}^{0}} \\
& y=1
\end{align}$
To find the value of the y-intercept, substitute $ x=-1$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{-1-2}} \\
& y={{3}^{-3}} \\
& y=\frac{1}{{{3}^{3}}}
\end{align}$
$ y=\frac{1}{27}$
To find the value of the y-intercept, substitute $ x=-2$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{-2-2}} \\
& y={{3}^{-4}} \\
& y=\frac{1}{{{3}^{4}}}
\end{align}$
$ y=\frac{1}{81}$
To find the value of the y-intercept, substitute $ x=3$ as given below:
$\begin{align}
& y={{3}^{x-2}} \\
& y={{3}^{3-2}} \\
& y={{3}^{1}} \\
& y=3
\end{align}$
Therefore, plot the intercepts $\left( 0,\frac{1}{9} \right),\left( 1,\frac{1}{3} \right)\text{,}\left( 2,1 \right)\text{,}\left( 3,3 \right)\text{,}\left( -1,\frac{1}{27} \right)\text{, and }\left( -2,\frac{1}{81} \right)$ and join them with a free hand in order to get the graph of the equation $ y={{3}^{x-2}}$
