Answer
The graph is shown below.
Work Step by Step
The inequality is
$x+2y\gt4$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$x+2y=4$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow x+2(0)=4$
Simplify.
$\Rightarrow x=4$
The $x−$intercept is $4$, so the line passes through $A=(4,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 0+2y=4$
Simplify.
$\Rightarrow 2y=4$
Divide both sides by $2$.
$\Rightarrow \frac{2y}{2}=\frac{4}{2}$
$\Rightarrow y=2$
The $y−$intercept is $2$, so the line passes through $B=(0,2)$.
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.
$\Rightarrow 0+2(0)\gt4$
Simplify.
$\Rightarrow 0\gt4$
The statement is not correct.
The solution set does contain the test point.
Hence, the upper part of the line is the solution set.
