Answer
See graph
Work Step by Step
We have to draw the graph of the following equation with $3$ variables;
$$2x+9y-3z=-18.$$
Find the $x$-intercept by setting $y=0$ and $z=0$ and solving the resulting equation:
$$2x=-18\Rightarrow x=-9$$
The $x$-intercept is $-9$, so we will plot the point $(-9,0,0)$.
Find the $y$-intercept by setting $x=0$ and $z=0$ and solving the resulting equation:
$$9y=-18\Rightarrow y=-2$$
The $y$-intercept is $2$, so we will plot the point $(0,2,0)$.
Find the $z$-intercept by setting $x=0$ and $y=0$ and solving the resulting equation:
$$-3z=-18\Rightarrow z=6$$
The $z$-intercept is $6$, so we will plot the point $(0,0,6)$.
We join the $3$ points and obtain a triangular region which is a part of the plane described by the given equation.
