Answer
The graph is shown below:
Work Step by Step
Let us consider the inequalities $ x-2y<8$; substitute the equals symbol in place of the inequality and rewrite the equation as given below:
By finding any two solutions of the linear equation, plot the graph of the linear equation
$ x-2y=8$:
To find the value of the x-intercept, substitute y = 0 as follows:
$\begin{align}
& x-2\left( 0 \right)=8 \\
& x=8 \\
\end{align}$
To find the value of the y-intercept, substitute x = 0 as follows:
$\begin{align}
& 0-2y=8 \\
& y=-4 \\
\end{align}$
Plot the intercepts $\left( 8,0 \right)\text{ and }\left( 0,-4 \right)$ and draw a dotted line passing through these points because the inequality does not contain the equal symbol.
Now this dashed line divides the plane in 3 region: the line itself, and the two half planes.
Now, take the origin $\left( 0,0 \right)$ as a test point and check the region in the graph to shade:
Check if the test point satisfies the inequality.
$ x-2y<8$
$0-2*0<8$
$0<8$
This is true, so the origin is included. See the final graph below.
