Intermediate Algebra, Chapter 3, Review Exercises, Section Review Exercises, Problem 38

Illustrate the solution set of the inequality $5x - y > 6$


To graph $5x - y > 6$ we must graph the boundary line $5x - y = 6$ first. To do this, we need to find the
intercepts of the line

$x$-intercept (set $y = 0$):

$
\begin{equation}
\begin{aligned}
5x - 0 &= 6\\
\\
5x &= 6 \\
\\
x &= \frac{6}{5}
\end{aligned}
\end{equation}
$


$y$-intercept (set $x = 0$):

$
\begin{equation}
\begin{aligned}
5(0) - y &= 6 \\
\\
-y &= 6\\
\\
y &= -6
\end{aligned}
\end{equation}
$

Now, by using test point. Let's say point $(2,-2)$ from the right of the boundary line.

$
\begin{equation}
\begin{aligned}
5x - y &> 6 \\
\\
5(2) - (-2) &> 6 \\
\\
10 + 2 &> 6 \\
\\
12 &> 6
\end{aligned}
\end{equation}
$

Since the inequality symbol is $>$, then the boundary line must be dashed.
Moreover, since the test point satisfy the inequality, then we must shade the right
portion of the boundary line. So the graph is,