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Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z= (Type expressions using t as the variable.) %3D

Find parametric equations for the line through (-4,1,1) parallel to the x-axis. Let z = 1. y-z= (Type expressions using t as the variable.) %3D

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Problem Statement:** Find parametric equations for the line through the point (-4, 1, 1) that is parallel to the x-axis. **Given:** - Let \( z = 1 \). **Parametric Equations Formulation:** - \( x = \) [ ] - \( y = \) [ ] - \( z = \) [ ] - \(-\infty < t < \infty\) (Type expressions using \( t \) as the variable.) **Explanation:** To find the parametric equations, we need to express each coordinate (x, y, z) in terms of a parameter \( t \). The line is parallel to the x-axis, so the y and z coordinates will remain constant at 1 as the line propagates along x. Therefore, the parametric equations will be: - \( x = -4 + t \) - \( y = 1 \) - \( z = 1 \) These equations represent a line extending in both directions along the x-axis through the point (-4, 1, 1).
Transcribed Image Text:**Problem Statement:** Find parametric equations for the line through the point (-4, 1, 1) that is parallel to the x-axis. **Given:** - Let \( z = 1 \). **Parametric Equations Formulation:** - \( x = \) [ ] - \( y = \) [ ] - \( z = \) [ ] - \(-\infty < t < \infty\) (Type expressions using \( t \) as the variable.) **Explanation:** To find the parametric equations, we need to express each coordinate (x, y, z) in terms of a parameter \( t \). The line is parallel to the x-axis, so the y and z coordinates will remain constant at 1 as the line propagates along x. Therefore, the parametric equations will be: - \( x = -4 + t \) - \( y = 1 \) - \( z = 1 \) These equations represent a line extending in both directions along the x-axis through the point (-4, 1, 1).
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