Answer
$x=3$, $y=-2$, see graph
Work Step by Step
Consider the linear equation given
$6x-9y-18=0$
Use intercepts to graph the equation as follows:
Step 1: Find the $x$ intercept of the graph.
Substitute $y=0$ in the equation $6x-9y-18=0$ and find the value of $x$
$\begin{align}
& 6x-9\times 0-18=0 \\
& 6x=18 \\
& x=\frac{18}{6} \\
& =3
\end{align}$
So, the $x$ intercept of the line $6x-9y-18=0$ is 3. Hence, the line passes through the point $\left( 3,0 \right)$.
Step 2: Find the $y$ intercept.
Substitute $x=0$ in the equation $6x-9y-18=0$ and find the value of $y$:
$\begin{align}
& 6\times 0-9y-18=0 \\
& -9y=18 \\
& y=\frac{18}{\left( -9 \right)} \\
& =-2
\end{align}$
So, the $y$ intercept of the line $6x-9y-18=0$ is $-2$. Hence, the line passes through the point $\left( 0,-2 \right)$.
Step 3: Graph the equation in the rectangular coordinate system.
Locate the two intercepts $\left( 3,0 \right)$ and $\left( 0,-2 \right)$. Connect them by a straight line. The graph of the given equation $6x-9y-18=0$ is as follows:
