Beginning Algebra With Applications, Chapter 5, 5.6, Section 5.6, Problem 22

Write the inequality of the given graph below:



The dashed line pass through the $x$-intercept $(3,0)$ and $y$-intercept $(0,2)$.
The shaded region is in the lower half plane. Then, the equation of hte line
with the given intercepts is represented by
$\displaystyle \frac{x}{a} + \frac{y}{a} = 1$
Where $a$ and $b$ are $x$ and $y$ intercepters respectively.

So, the equation of the line is

$
\begin{equation}
\begin{aligned}
\frac{x}{3} + \frac{y}{2} &= 1\\
\\
\frac{2(x) + 3(y)}{6} &= 1 \\
\\
2x + 3y &= 6 \\
\\
3y &= -2x + 6 \\
\\
y &= \frac{-2x}{3} + 2
\end{aligned}
\end{equation}
$


Therefore, the equation of the inequality is,
$\displaystyle y < - \frac{2x}{3} + 2 $