Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) Point Slope (-3, 5) m is undefined (x, y) = ( (x, v) = ( (x, y) = (

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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## Finding Additional Points on a Line with an Undefined Slope

### Problem Statement
Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.)

### Given:
- **Point:** (-3, 5)
- **Slope:** \( m \) is undefined

### Task:
Find three additional points (x, y) that lie on the line.

### Solution:
#### Point 1:
(x, y) = (_____, _____)

#### Point 2:
(x, y) = (_____, _____)

#### Point 3:
(x, y) = (_____, _____)

### Analysis:
Since the slope \( m \) is undefined, this indicates that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can be any value. So the additional points will have the same x-coordinate as the given point, which is -3, and different y-coordinates.

Example points could include:
(x, y) = (-3, 6)
(x, y) = (-3, 7)
(x, y) = (-3, 8)

These points illustrate that regardless of the y-coordinate, the x-coordinate remains -3 in a vertical line with an undefined slope.
Transcribed Image Text:## Finding Additional Points on a Line with an Undefined Slope ### Problem Statement Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) ### Given: - **Point:** (-3, 5) - **Slope:** \( m \) is undefined ### Task: Find three additional points (x, y) that lie on the line. ### Solution: #### Point 1: (x, y) = (_____, _____) #### Point 2: (x, y) = (_____, _____) #### Point 3: (x, y) = (_____, _____) ### Analysis: Since the slope \( m \) is undefined, this indicates that the line is vertical. In a vertical line, the x-coordinate remains constant while the y-coordinate can be any value. So the additional points will have the same x-coordinate as the given point, which is -3, and different y-coordinates. Example points could include: (x, y) = (-3, 6) (x, y) = (-3, 7) (x, y) = (-3, 8) These points illustrate that regardless of the y-coordinate, the x-coordinate remains -3 in a vertical line with an undefined slope.
### Using a Point and Slope to Determine Additional Points on a Line

**Instructions:**
Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.)

**Given:**

- **Point:** \((4, 4)\)
- **Slope:** \( m = 0 \)

Since the slope \( m = 0 \) indicates a horizontal line, the y-coordinate of any point on this line will be constant and equal to 4. You can choose any x-value to find additional points on the line.

**Additional Points:**

Select any x-values and always use \( y = 4 \):

1. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \)
2. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \)
3. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \)

For instance, you can select:
1. \( (x, y) = (2, 4) \)
2. \( (x, y) = (6, 4) \)
3. \( (x, y) = (8, 4) \)

**Explanation of Graph/Diagram (if applicable):**

This problem presents a horizontal line passing through the point \((4, 4)\) with a slope of 0. A horizontal line has an identical y-coordinate for all points, thus irrespective of the x-value chosen, the y-coordinate will always be 4. 

Feel free to choose any other x-values to form different points along the given horizontal line.
Transcribed Image Text:### Using a Point and Slope to Determine Additional Points on a Line **Instructions:** Use the point on the line and the slope of the line to find three additional points that the line passes through. (There is more than one correct answer.) **Given:** - **Point:** \((4, 4)\) - **Slope:** \( m = 0 \) Since the slope \( m = 0 \) indicates a horizontal line, the y-coordinate of any point on this line will be constant and equal to 4. You can choose any x-value to find additional points on the line. **Additional Points:** Select any x-values and always use \( y = 4 \): 1. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \) 2. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \) 3. \( (x, y) = ( \_\_\_\_\_\ , \_\_\_\_\_\ ) \) For instance, you can select: 1. \( (x, y) = (2, 4) \) 2. \( (x, y) = (6, 4) \) 3. \( (x, y) = (8, 4) \) **Explanation of Graph/Diagram (if applicable):** This problem presents a horizontal line passing through the point \((4, 4)\) with a slope of 0. A horizontal line has an identical y-coordinate for all points, thus irrespective of the x-value chosen, the y-coordinate will always be 4. Feel free to choose any other x-values to form different points along the given horizontal line.
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