Answer
The graph is shown below.
Work Step by Step
The given inequality is
$\Rightarrow 4x-5y\geq20$.
Step 1:- Replace the inequality symbol
$\Rightarrow 4x-5y=20$.
Plug $y=0$ into the linear equation.
$\Rightarrow 4x-5(0)=20$.
$\Rightarrow 4x=20$
Divide both sides by $4$.
$\Rightarrow \frac{4x}{4}=\frac{20}{4}$
Simplify.
$\Rightarrow x=5$
The $x-$ intercept is $5$, so the line passes through $A=(5,0)$.
Plug $x=0$ into the linear equation.
$\Rightarrow 4(0)-5y=20$.
$\Rightarrow -5y=20$
Divide both sides by $-5$.
$\Rightarrow \frac{-5y}{-5}=\frac{20}{-5}$
Simplify.
$\Rightarrow y=-4$
The $y-$ intercept is $-4$, so the line passes through $B=(0,-4)$.
Draw a solid line through these two points because equality is included.
Step 2:- Choose a test point.
Let the test point be $C=(0,0)$.
Substitute the test point into the given inequality.
$\Rightarrow 4(0)-5(0)\geq20$.
Simplify.
$\Rightarrow 0\geq20$. The statement is false.
Shade the half-plane not containing the test point.
