Answer
See graph
Work Step by Step
We have to draw the graph of the following equation with $3$ variables;
$$-7x+7y+2z=14.$$
Find the $x$-intercept by setting $y=0$ and $z=0$ and solving the resulting equation:
$$-7x=14\Rightarrow x=-2$$
The $x$-intercept is $-2$, so we will plot the point $(-2,0,0)$.
Find the $y$-intercept by setting $x=0$ and $z=0$ and solving the resulting equation:
$$7y=14\Rightarrow y=2$$
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:
$$2z=14\Rightarrow z=7$$
The $z$-intercept is $7$, so we will plot the point $(0,0,7)$.
We join the $3$ points and obtain a triangular region which is a part of the plane described by the given equation.
