Answer
The graph is shown below.
Work Step by Step
The inequality is
$x+y\geq3$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$x+y=3$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow x+0=3$
$\Rightarrow x=3$
The $x−$intercept is $3$, so the line passes through $A=(3,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow 0+y=3$
Simplify.
$\Rightarrow y=3$
The $y−$intercept is $3$, so the line passes through $B=(0,3)$.
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.
$\Rightarrow 0+0\geq3$
Simplify.
$\Rightarrow 0\geq3$
The statement is false.
The solution set does not contain the test point.
Hence, the upper part of the line is the solution set.
