Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 116

Graph $3x-2y=-6$ using a graphing device. Verify that the graph has the correct $x-$ and $y$-intercepts.







$x$-intercept:


$
\begin{equation}
\begin{aligned}

3x-2y=& -6
&& \text{Given equation}
\\
3x-2(0) =& -6
&& \text{To find the $x$-intercept, let } y = 0
\\
3x =& -6
&& \text{Divide by } 3
\\
x =& -2
&&

\end{aligned}
\end{equation}
$


The $x$-intercept is $(-2,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

3x-2y=& -6
&& \text{Given equation}
\\
3(0)-2y=& -6
&& \text{To find the $y$-intercept, let } x=0
\\
-2y =& -6
&& \text{Divide by } -2
\\
y =& 3
&&

\end{aligned}
\end{equation}
$



The $y$-intercept is $(0,3)$