   Chapter 12.5, Problem 43E

Chapter
Section
Textbook Problem

# Use intercepts to help sketch the plane.43. 6x − 3y + 4z = 6

To determine

To sketch: The plane 6x3y+4z=6 with the use of intercepts.

Explanation

Write the equation of the plane as follows.

6x3y+4z=6 (1)

The plane is sketched in the three-dimensional coordinate system by determining the x-, y-, and z-intercepts.

Calculation of x-intercept in the plane:

The x-intercept in the plane is determined by setting the y- and z-coordinate values as zero.

y=0z=0

Substitute 0 for y and 0 for z in equation (1),

6x3(0)+4(0)=66x=6x=1

Therefore, the x-intercept in the plane is (1,0,0) .

Calculation of y-intercept in the plane:

The y-intercept in the plane is determined by setting the x- and z-coordinate values as zero.

x=0z=0

Substitute 0 for x and 0 for z in equation (1),

6(0)3y+4(0)=63y=6y=2

Therefore, the y-intercept in the plane is (0,2,0)

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