Chapter 12.5, Problem 43E

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8th Edition

James Stewart

ISBN: 9781305266643

Textbook Problem

Use intercepts to help sketch the plane.

**43.** 6*x* − 3*y* + 4*z* = 6

To determine

**To sketch:** The plane

Explanation

Write the equation of the plane as follows.

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.

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

Therefore, the *x*-intercept in the plane is

**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.

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

Therefore, the *y*-intercept in the plane is

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