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.