Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 102

Graph $2x-3y = -6$ by using $x$- and $y$-intercepts

$x$-intercept:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


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

$y$-intercept:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$



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

Graph the ordered pairs $(-3,0)$ and $(0,2)$. Draw a straight line through the points.