Answer
$y=-x+5$
(see graph below)
Work Step by Step
Using the properties of equality, the Slope-Intercept Form ($y=mx+b$) of the given equation, $
3y+3x=15
,$ is
\begin{align*}\require{cancel}
3y+3x&=15
\\
3y+3x-3x&=15-3x
\\
3y&=-3x+15
\\\\
\dfrac{3y}{3}&=\dfrac{-3x+15}{3}
\\\\
y&=\dfrac{-3x}{3}+\dfrac{15}{3}
\\\\
y&=-x+5
.\end{align*}
To graph the given equation, use the intercepts.
If $y=0,$ then
\begin{align*}
3(0)+3x&=15
\\
3x&=15
\\\\
\dfrac{3x}{3}&=\dfrac{15}{3}
\\\\
x&=5
.\end{align*}
The $x$-intercept is $
\left( 5,0 \right)
$.
If $x=0,$ then
\begin{align*}
3y+3(0)&=15
\\
3y&=15
\\\\
\dfrac{3y}{3}&=\dfrac{15}{3}
\\\\
y&=5
.\end{align*}
The $y$-intercept is $
\left( 0,5 \right)
$.
Connecting the intercepts with a line, the graph of the given equation is shown above.
