Answer
The graph is shown below.
Work Step by Step
The inequality is
$\frac{x}{2}+\frac{y}{3}\lt1$
Step 1:- Replace the inequality symbol with $=$ and graph the linear equation.
$\frac{x}{2}+\frac{y}{3}=1$
Plug $y=0$ for the $x−$intercept.
$\Rightarrow \frac{x}{2}+\frac{(0)}{3}=1$
Simplify.
$\Rightarrow \frac{x}{2}=1$
Multiply both sides by $2$.
$\Rightarrow 2\cdot \frac{x}{2}=2\cdot1$
Simplify.
$\Rightarrow x=2$
The $x−$intercept is $2$, so the line passes through $A=(2,0)$.
Plug $x=0$ for the $y−$intercept.
$\Rightarrow \frac{(0)}{2}+\frac{y}{3}=1$
Simplify.
$\Rightarrow \frac{y}{3}=1$
Multiply both sides by $3$.
$\Rightarrow 3\cdot \frac{y}{3}=3\cdot 1$
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.
$\Rightarrow \frac{(0)}{2}+\frac{(0)}{3}\lt1$
Simplify.
$\Rightarrow 0\lt1$
The statement is correct.
The solution set contains the test point.
Hence, the upper part of the line is the solution set.
