   Chapter 7.2, Problem 1CP ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
1 views

# Find the x-, y-, and z-intercepts of the plane 2 x +   4 y +   z   =   8. Then sketch the plane.

To determine

To calculate: The x-intercept, y-intercept and z-intercept of the plane, 2x+4y+z=8 and sketch the plane.

Explanation

Given information:

The equation of plane is 2x+4y+z=8.

Formula used:

The general equation of plane,

ax+by+cz=d

The x-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for y and 0 for z, the y-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for x and 0 for z and the z-intercept of the plane, ax+by+cz=d can be calculated by substituting 0 for x and 0 for y, where a, b and c not all zero.

Calculation:

Consider equation of plane,

2x+4y+z=8 ...... (1)

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

2x+4(0)+(0)=82x=8x=4

Hence, the x-intercept of the plane, 2x+4y+z=8 is (4,0,0).

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

2(0)+4y+(0)=84y=8y=2

Hence, the y-intercept of the plane, 2x+4y+z=8 is (0,2,0).

Substitute, 0 for x and 0 for y in equation (1).

2(0)+4(0)+z=8z=8

Hence, the z-intercept of the plane, 2x+4y+z=8 is (0,0,8)

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