Answer
See graph
Work Step by Step
We have to draw the graph of the following equation with $3$ variables;
$$x+5y+3z=15.$$
Find the $x$-intercept by setting $y=0$ and $z=0$ and solving the resulting equation:
$$x=15\Rightarrow x=15$$
The $x$-intercept is $15$, so we will plot the point $(15,0,0)$.
Find the $y$-intercept by setting $x=0$ and $z=0$ and solving the resulting equation:
$$5y=15\Rightarrow y=3$$
The $y$-intercept is $3$, so we will plot the point $(0,3,0)$.
Find the $z$-intercept by setting $x=0$ and $y=0$ and solving the resulting equation:
$$3z=15\Rightarrow z=5$$
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 graph of the given equation that lies in the first octant.
