O Which of these Is the equatión of the line passing through a HORIZONTAL line? the points (-2,-4) and (5,10) O Find the slope m,of O which of these is the equa trón of the line with slope mz- passing through c0,6) ? Ai 2x-3y =6 2 A: A: y= 7 B: B: x = 5 B: 3x - 2y a 12 C: ċ: 2x+3y = 18 D: NONE OF THESE D: NONE OF THESE D: NO NE OF THESE

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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**Transcription and Explanation for Educational Use**

This image contains a series of questions related to linear equations and graph interpretation. Below is a transcription of each question along with detailed explanations where necessary.

**Question 1:**  
Which of these is the equation of a HORIZONTAL line?  
A: \( y = x \)  
B: \( y = 7 \)  
C: \( x = 5 \)  
D: NONE OF THESE  

*Explanation*:  
A horizontal line has a constant \( y \)-value for all \( x \)-values, so the equation is of the form \( y = \text{{constant}} \). The correct answer is B: \( y = 7 \).

---

**Question 2:**  
Find the slope \( m \) of the line passing through the points \((-2, -4)\) and \( (5, 10) \).  
A: \( m = -\frac{2}{5} \)  
B: \( m = \frac{5}{2} \)  
C: \( m = 2 \)  
D: NONE OF THESE  

*Solution*:  
- The slope \( m \) is calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \).  
- Substituting the values: \( m = \frac{10 - (-4)}{5 - (-2)} = \frac{14}{7} = 2 \).  
- The correct answer is C: \( m = 2 \).

---

**Question 3:**  
Which of these is the equation of the line with slope \( m = \frac{2}{3} \) passing through \((0, 6)\)?  
A: \( 2x - 3y = 6 \)  
B: \( 3x - 2y = 12 \)  
C: \( 2x + 3y = 18 \)  
D: NONE OF THESE  

*Solution*:  
- Using point-slope form \( y - y_1 = m(x - x_1) \), the equation becomes \( y - 6 = \frac{2}{3}(x - 0) \). Simplifying, \( y = \frac{2}{3}x + 6 \) which is none of the given choices.
- The correct answer
Transcribed Image Text:**Transcription and Explanation for Educational Use** This image contains a series of questions related to linear equations and graph interpretation. Below is a transcription of each question along with detailed explanations where necessary. **Question 1:** Which of these is the equation of a HORIZONTAL line? A: \( y = x \) B: \( y = 7 \) C: \( x = 5 \) D: NONE OF THESE *Explanation*: A horizontal line has a constant \( y \)-value for all \( x \)-values, so the equation is of the form \( y = \text{{constant}} \). The correct answer is B: \( y = 7 \). --- **Question 2:** Find the slope \( m \) of the line passing through the points \((-2, -4)\) and \( (5, 10) \). A: \( m = -\frac{2}{5} \) B: \( m = \frac{5}{2} \) C: \( m = 2 \) D: NONE OF THESE *Solution*: - The slope \( m \) is calculated using the formula \( m = \frac{y_2 - y_1}{x_2 - x_1} \). - Substituting the values: \( m = \frac{10 - (-4)}{5 - (-2)} = \frac{14}{7} = 2 \). - The correct answer is C: \( m = 2 \). --- **Question 3:** Which of these is the equation of the line with slope \( m = \frac{2}{3} \) passing through \((0, 6)\)? A: \( 2x - 3y = 6 \) B: \( 3x - 2y = 12 \) C: \( 2x + 3y = 18 \) D: NONE OF THESE *Solution*: - Using point-slope form \( y - y_1 = m(x - x_1) \), the equation becomes \( y - 6 = \frac{2}{3}(x - 0) \). Simplifying, \( y = \frac{2}{3}x + 6 \) which is none of the given choices. - The correct answer
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