Answer
The graph is shown below.
Work Step by Step
The inequality is
$2x+y\gt6$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$2x+y=6$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow 2x+0=6$
Simplify.
$\Rightarrow 2x=6$
Divide both sides by $2$.
$\Rightarrow \frac{2x}{2}=\frac{6}{2}$
Simplify.
$\Rightarrow x=3$
The $x−$intercept is $3$, so the line passes through $A=(3,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 2(0)+y=6$
Simplify.
$\Rightarrow y=6$
The $y−$intercept is $6$, so the line passes through $B=(0,6)$.
Draw a straight line through these intercept points.
Step 2:- Choose a test point and plug into the inequality.
Let the test point $C=(0,0)$.
Plug the test point into inequality.
$\Rightarrow 2(0)+0\gt6$
Simplify.
$\Rightarrow 0\gt6$
The statement is not correct.
The solution set does contain the test point.
Hence, the upper part of the line is the solution set.