Answer
See below:
Work Step by Step
Step 1: Convert the inequality to an equation by replacing > by = sign.
\[2x-7y=14\]
Step 2: Graph the equation using intercept form or slope-intercept form.
Make \[x=0\] to find the y-intercept,
\[\begin{align}
& 2x-7y=14 \\
& 0-7y=14 \\
& y=-2
\end{align}\]
Make \[y=0\] to find x-intercept,
\[\begin{align}
& 2x-7y=14 \\
& 2x-0=14 \\
& x=7
\end{align}\]
The line passes through \[\left( -2,0 \right)\]and \[\left( 0,7 \right)\]. The line is dashed since the inequality contains the > symbol.
Step 3: Choose a test point. The origin \[\left( 0,0 \right)\]be the test point. Substituting in the inequality
\[\begin{align}
& 2x-7y>14 \\
& 0>14
\end{align}\]
The statement is false. The graph does not contain the test point.
