Beginning Algebra With Applications, Chapter 5, 5.6, Section 5.6, Problem 26

Illustrate the solution set $y + 3 < 6 (x + 1)$

$
\begin{equation}
\begin{aligned}
y + 3 &< 6x + 6
&& \text{Solve the inequality for } y \\
\\
y &< 6x + 6 - 3\\
\\
y &< 6x + 3
\end{aligned}
\end{equation}
$


To graph the inequality, we first find the intercepts of the line $y = 6x + 3$.
In this case, the $x$-intercept (set $y = 0$) is $\displaystyle \left( -\frac{1}{2}, 0 \right)$

$
\begin{equation}
\begin{aligned}
0 &= 6x + 3 \\
\\
6x &= -3 \\
\\
x &= -\frac{1}{2}
\end{aligned}
\end{equation}
$


And, the $y$-intercept (set $x = 0$) is $(0,3)$

$
\begin{equation}
\begin{aligned}
y &= 6(0) + 3\\
\\
y &= 3
\end{aligned}
\end{equation}
$


So, the graph is



Graph $y = 6x + 3$ as a dashed line. Shade the lower half-plane.