   Chapter 12.5, Problem 41E

Chapter
Section
Textbook Problem

# Use intercepts to help sketch the plane.41. 2x + 5y + z = 10

To determine

To sketch: The plane 2x+5y+z=10 with the use of intercepts.

Explanation

Write the equation of the plane as follows:

2x+5y+z=10 (1)

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

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),

2x+5(0)+(0)=102x=10x=5

Therefore, the x-intercept in the plane is (5,0,0).

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),

2(0)+5y+(0)=105y=10y=2

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

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