Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 10, Problem 17CT
To determine

To draw: The graph of the plane 3x+6y+2z=18 and label the intercepts.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given information:

The equation of the plane is 3x+6y+2z=18 .

Graph:

The graph of the plane 3x+6y+2z=18 is shown below.

  Precalculus with Limits: A Graphing Approach, Chapter 10, Problem 17CT , additional homework tip 1

Interpretation:

To calculate the intercepts of the plane, substitute the values of x , y and z as zero.

Substitute z=0 in the equation of the plane to calculate the intercept with xy -plane.

  3x+6y+2(0)=183x+6y=18x+2y=6

From the above, the line intercepts the x -axis at (6,0,0) and the y -axis at (0,3,0) .

Similarly, substitute y=0 in the equation of the plane to calculate the intercept with xz -plane.

  3x+6(0)+2z=183x+2z=18

From the above, the line intercepts the x -axis at (6,0,0) and the z -axis at (0,0,9) .

Similarly, substitute x=0 in the equation of the plane to calculate the intercept with yz -plane.

  3(0)+6y+2z=183y+z=9

From the above, the line intercepts the y -axis at (0,3,0) and the z -axis at (0,0,9) .

Plot these points on the graph.

  Precalculus with Limits: A Graphing Approach, Chapter 10, Problem 17CT , additional homework tip 2

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Chapter 10, Problem 16CT
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Chapter 10, Problem 18CT

Chapter 10 Solutions

Precalculus with Limits: A Graphing Approach

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