Beginning Algebra With Applications, Chapter 5, Test, Section Test, Problem 10

Illustrate the solution set of $2x - y \geq 2$

$
\begin{equation}
\begin{aligned}
2x - y &\geq 2\\
\\
-y &\geq - 2x + 2
&& \text{Solve the inequality for } y \\
\\
\frac{-y}{-1} &\leq \frac{-2x}{-1} + \frac{2}{-1}
&& \text{Remember that if you divide or multiply negative numbers ,the inequality symbol reverses}\\
\\
y &\leq 2x - 2
\end{aligned}
\end{equation}
$


To graph the inequality, we first find the intercepts of the line $y = 2x - 2$.
In this case, the $x$-intercept (set $y = 0$) is $(1,0)$

$
\begin{equation}
\begin{aligned}
0 &= 2x - 2\\
\\
2x &= 2\\
\\
x &= 1
\end{aligned}
\end{equation}
$

And the $y$-intercept (set $x = 0$) is $(0,-2)$

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

So the graph is



Graph $y = 2x - 2$ as a solid line. Shade the lower half of the plane.