Answer
$y=\dfrac{2}{3}x+3$
(See graph below.)
Work Step by Step
Using the properties of equality, the Slope-Intercept Form ($y=mx+b$) of the given equation, $
-4x+6y=18
,$ is
\begin{align*}\require{cancel}
-4x+6y&=18
\\
-4x+6y+4x&=18+4x
\\
6y&=4x+18
\\\\
\dfrac{6y}{6}&=\dfrac{4x+18}{6}
\\\\
y&=\dfrac{4x+18}{6}
\\\\
y&=\dfrac{4x}{6}+\dfrac{18}{6}
\\\\
y&=\dfrac{\cancel4^2x}{\cancel6^3}+3
\\\\
y&=\dfrac{2x}{3}+3
\\\\
y&=\dfrac{2}{3}x+3
.\end{align*}
To graph the given equation, use the intercepts.
If $y=0,$ then
\begin{align*}
-4x+6(0)&=18
\\
-4x&=18
\\\\
\dfrac{-4x}{-4}&=\dfrac{18}{-4}
\\\\
x&=\dfrac{18}{-4}
\\\\
x&=\dfrac{\cancel{18}^9}{\cancel{-4}^{-2}}
\\\\
x&=\dfrac{9}{-2}
\\\\
x&=-\dfrac{9}{2}
.\end{align*}
The $x$-intercept is $
\left( -\dfrac{9}{2},0 \right)
$.
If $x=0,$ then
\begin{align*}
-4(0)+6y&=18
\\
6y&=18
\\\\
\dfrac{6y}{6}&=\dfrac{18}{6}
\\\\
y&=3
.\end{align*}
The $y$-intercept is $
\left( 0,3\right)
$.
Connecting the intercepts with a line, the graph of the given equation is shown above.
