Elementary Geometry for College Students (6th Edition)

Published by Brooks Cole
ISBN 10:
ISBN 13:

Chapter 10 - Section 10.6 - The Three-Dimensional Coordinate System - Exercises - Page 482: 19

Answer

The x-intercept is $(6,0,0)$ The y-intercept is $(0,3,0)$ The z-intercept is $(0,0,6)$ We can see a sketch of the plane.
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Work Step by Step

$x+2y+z = 6$ We can find the x-intercept when $y=0$ and $z = 0$: $x+2y+z = 6$ $x+2(0)+(0) = 6$ $x = 6$ The x-intercept is $(6,0,0)$ We can find the y-intercept when $x=0$ and $z = 0$: $x+2y+z = 6$ $(0)+2y+(0) = 6$ $y = 3$ The y-intercept is $(0,3,0)$ We can find the z-intercept when $x=0$ and $y = 0$: $x+2y+z = 6$ $(0)+2(0)+z = 6$ $z = 6$ The z-intercept is $(0,0,6)$ We can plot these three points on the graph. Then we can connect these three points to sketch the plane for the equation.
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