Answer
See graph
Work Step by Step
We have to draw the graph of the following equation with $3$ variables;
$$5x-y-2z=10.$$
Find the $x$-intercept by setting $y=0$ and $z=0$ and solving the resulting equation:
$$5x=10\Rightarrow x=2$$
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:
$$-y=10\Rightarrow y=-10$$
The $y$-intercept is $-10$, so we will plot the point $(0,-10,0)$.
Find the $z$-intercept by setting $x=0$ and $y=0$ and solving the resulting equation:
$$-2z=10\Rightarrow z=-5$$
The $z$-intercept is $-5$, so we will plot the point $(0,0,-5)$.
We join the $3$ points and obtain a triangular region which is a part of the plane described by the given equation.
