Intermediate Algebra, Chapter 3, 3.1, Section 3.1, Problem 52

Determine the $x$- and $y$-intercepts. Then graph the equation $x - 3y = 0$.

To find $x$-intercept, we set $y = 0$


$
\begin{equation}
\begin{aligned}

x - 3(0) =& 0 \\
x =& 0

\end{aligned}
\end{equation}
$


To find $y$-intercept, we set $x = 0$


$
\begin{equation}
\begin{aligned}

0 - 3y =& 0 \\
-3y =& 0 \\
y =& 0

\end{aligned}
\end{equation}
$


Both intercepts are the same point, $(0,0)$ which means that the graph passes through the origin. To find another point, choose any nonzero number for $x$ or $y$ and solve for the other variable. We choose $x = 3$.


$
\begin{equation}
\begin{aligned}

x - 3y =& 0 \\
3 - 3y =& 0 \\
-3y =& -3 \\
y =& 1

\end{aligned}
\end{equation}
$


This gives to ordered pair $(3,1)$. So the graph is