Algebra 2 (1st Edition)

Published by McDougal Littell
ISBN 10: 0618595414
ISBN 13: 978-0-61859-541-9

Chapter 3 Linear Systems and Matrices - Investigating Algebra Activity - 3.4 Graphing Linear Equations in Three Variables - Draw Conclusions - Page 177: 1

Answer

See graph

Work Step by Step

We have to draw the graph of the following equation with $3$ variables; $$4x+3y+2z=12.$$ Find the $x$-intercept by setting $y=0$ and $z=0$ and solving the resulting equation: $$4x=12\Rightarrow x=3$$ The $x$-intercept is $3$, so we will plot the point $(4,0,0)$. Find the $y$-intercept by setting $x=0$ and $z=0$ and solving the resulting equation: $$3y=12\Rightarrow y=4$$ The $y$-intercept is $4$, so we will plot the point $(0,4,0)$. Find the $z$-intercept by setting $x=0$ and $y=0$ and solving the resulting equation: $$2z=12\Rightarrow z=6$$ 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 graph of the given equation that lies in the first octant.
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