   Chapter 12, Problem 32RE

Chapter
Section
Textbook Problem

# Identify and sketch the graph of each surface.32. 4x − y + 2z = 4

To determine

To identify and sketch: The surface equation 4xy+2z=4 .

Explanation

Given data:

Surface equation is 4xy+2z=4 .

Write the surface equation of the plane as follows.

4xy+2z=4 (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),

4x(0)+2(0)=44x=4x=44x=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

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