Beginning Algebra With Applications, Chapter 5, 5.6, Section 5.6, Problem 8

Illustrate the solution set $\displaystyle y \leq -\frac{5}{2} - 4$
To graph the inequality, we first find the intercepts of the line $\displaystyle y = - \frac{5}{2}x - 4$.
In this case, the $x$-intercept (set $y = 0$) is $\displaystyle \left( -\frac{8}{5}, 0 \right)$


$
\begin{equation}
\begin{aligned}
0 &= -\frac{5}{2} x - 4\\
\\
\frac{5}{2}x &= -4\\
\\
x &= -\frac{8}{5}
\end{aligned}
\end{equation}
$


And the $y$-intercept (set $x = 0$) is $(0, -4)$

$
\begin{equation}
\begin{aligned}
y &= -\frac{5}{2}(0) - 4\\
\\
y &= - 4
\end{aligned}
\end{equation}
$

So the graph is


Graph is $\displaystyle y = -\frac{5}{2} x - 4 $ as a solid line. Shade the lower half-plane.