Beginning Algebra With Applications, Chapter 5, 5.2, Section 5.2, Problem 100

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

$x$-intercept:


$
\begin{equation}
\begin{aligned}

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

\end{aligned}
\end{equation}
$


The $x$-intercept is $(6,0)$

$y$-intercept:


$
\begin{equation}
\begin{aligned}

x-3y =& 6
&& \text{Given equation}
\\
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 $(6,0)$ and $(0,-2)$. Draw a straight line through the points.