Answer
$y=-\dfrac{1}{3}x+\dfrac{5}{3}
$
(see graph below)
Work Step by Step
Using the properties of equality, the Slope-Intercept Form ($y=mx+b$) of the given equation, $
3y+x=5
,$ is
\begin{align*}\require{cancel}
3y+x-x&=5-x
\\
3y&=-x+5
\\\\
\dfrac{3y}{3}&=\dfrac{-x+5}{3}
\\\\
y&=\dfrac{-x}{3}+\dfrac{5}{3}
\\\\
y&=-\dfrac{1}{3}x+\dfrac{5}{3}
.\end{align*}
To graph the given equation, use the intercepts.
If $y=0,$ then
\begin{align*}
3(0)+x&=5
\\
x&=5
.\end{align*}
The $x$-intercept is $
\left( 5,0 \right)
$.
If $x=0,$ then
\begin{align*}
3y+0&=5
\\
3y&=5
\\\\
\dfrac{3y}{3}&=\dfrac{5}{3}
\\\\
y&=\dfrac{5}{3}
.\end{align*}
The $y$-intercept is $
\left( 0,\dfrac{5}{3} \right)
$.
Connecting the intercepts with a line, the graph of the given equation is shown above.
