Answer
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
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}
\\&-4x+3y&=&12
\\&-4x+3(0)&=&12
\\&-4x&=&12
\\&\frac{-4x}{-4}&=&\frac{12}{-4}
\\&x&=&-3
\end{array}
The x-intercept is $(-3, 0)$.
Find the x-intercept of the given equation. Set $x=0$ then solve for $y$ to obtain:
\begin{array}{ccc}
\\&-4x+3y&=&12
\\&-4(0)+3y&=&12
\\&3y&=&12
\\&\frac{3y}{3}&=&\frac{12}{3}
\\&y&=&4
\end{array}
The y-intercept is $(0, 4)$.
Graph the line by plotting the intercepts 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 $(-\infty, +\infty)$.
