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Determine whether the pair of lines is parallel, perpendicular, or neither. 9x + 3y = 12 27x + 9y = 38 O A. Parallel O B. Perpendicular OC. Neither

Determine whether the pair of lines is parallel, perpendicular, or neither. 9x + 3y = 12 27x + 9y = 38 O A. Parallel O B. Perpendicular OC. Neither

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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### Determine the Relationship Between Two Lines **Question:** Determine whether the pair of lines is parallel, perpendicular, or neither. \[ 9x + 3y = 12 \] \[ 27x + 9y = 38 \] **Options:** - **A. Parallel** - **B. Perpendicular** - **C. Neither** **Instructions:** Choose the correct option based on the given equations of the lines. **Explanation:** To determine whether the lines are parallel, perpendicular, or neither, you need to compare their slopes. Convert each equation into slope-intercept form (y = mx + b) where **m** is the slope. 1. For the first equation: \[ 9x + 3y = 12 \] - Isolate \(y\): \[ 3y = -9x + 12 \] \[ y = -3x + 4 \] - The slope \((m_1)\) is \(-3\). 2. For the second equation: \[ 27x + 9y = 38 \] - Isolate \(y\): \[ 9y = -27x + 38 \] \[ y = -3x + \frac{38}{9} \] - The slope \((m_2)\) is also \(-3\). **Conclusion:** Since the slopes of both lines are equal \((-3)\), the lines are parallel. **Correct Answer:** - **A. Parallel**
Transcribed Image Text:### Determine the Relationship Between Two Lines **Question:** Determine whether the pair of lines is parallel, perpendicular, or neither. \[ 9x + 3y = 12 \] \[ 27x + 9y = 38 \] **Options:** - **A. Parallel** - **B. Perpendicular** - **C. Neither** **Instructions:** Choose the correct option based on the given equations of the lines. **Explanation:** To determine whether the lines are parallel, perpendicular, or neither, you need to compare their slopes. Convert each equation into slope-intercept form (y = mx + b) where **m** is the slope. 1. For the first equation: \[ 9x + 3y = 12 \] - Isolate \(y\): \[ 3y = -9x + 12 \] \[ y = -3x + 4 \] - The slope \((m_1)\) is \(-3\). 2. For the second equation: \[ 27x + 9y = 38 \] - Isolate \(y\): \[ 9y = -27x + 38 \] \[ y = -3x + \frac{38}{9} \] - The slope \((m_2)\) is also \(-3\). **Conclusion:** Since the slopes of both lines are equal \((-3)\), the lines are parallel. **Correct Answer:** - **A. Parallel**
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