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: 2

Answer

See graph

Work Step by Step

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