Answer
domain: $(−\infty,+\infty)$
range: $(−\infty,+\infty)$
Refer to the graph below.
Work Step by Step
The given line can be graphed using the x and y-intercepts.
RECALL:
(1) The x-intercept can be found by setting y=0 then solving for x.
(2) The y-intercept can be found by setting x=0 then solving for y.
Find the x-intercept of the given equation. Set y=0 then solve for x to obtain:
\begin{array}{ccc}
&3x+2y&=&0
\\&3x+2(0)&=&0
\\&3x&=&=0
\\&\frac{3x}{3}&=&\frac{0}{3}
\\&x&=&0\end{array}
The x-intercept is $(0,0)$.
Find the y-intercept of the given equation. Set x=0 then solve for y to obtain:
\begin{array}{ccc}
&3x+2y&=&0
\\&3(0)+2y&=&0
\\&2y&=&=0
\\&\frac{2y}{2}&=&\frac{0}{2}
\\&y&=&0\end{array}
The y-intercept is $(0,0)$.
The intercepts are the same so one more point is needed to graph the line.
Set $x=2$ then solve for y to obtain:
$3x+2y=0
\\3(2)+2y=0
\\6+2y=0
\\6+2y-6=0-6
\\2y=-6
\\\frac{2y}{2}=\frac{-6}{2}
\\y=-3$
The line contains the point (2, -3).
Graph the line by plotting $(0,0)$ and $(2, -3)$ and connecting them using a line.
(Refer to the graph in the answer part above.)
The graph covers all x-values therefore the domain is $(−\infty,+\infty)$.
The graph covers all y-values therefore the range is $(−\infty,+\infty)$.
