Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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pull down options are 0, 1, -1, 9/7, undefined.
![**Understanding Vertical Lines and Their Equations**
When dealing with vertical lines in a coordinate plane, there are specific characteristics and formulas that define them.
1. **The Slope of a Vertical Line:**
Vertical lines have a unique property where their slope is undefined. This is due to the fact that vertical lines rise infinitely without running horizontally, which causes the denominator in the slope formula (rise over run) to be zero, thus making the slope undefined.
In the provided interface, you will see a dropdown menu next to the text "The slope of a vertical line is". You need to select the appropriate term such as "undefined" from the dropdown in this scenario.
2. **The Equation of a Vertical Line:**
The equation of a vertical line is derived based on the constant x-value through which the line passes. For example, if a vertical line passes through the point (7, 9), the equation of the line is \( x = 7 \). This is because all points on this vertical line will have the same x-coordinate, which is 7.
In the provided interface, you will see a space next to the text "The equation of the vertical line passing through (7, 9) is". You should enter and confirm the equation \( x = 7 \) in this space.
**Example:**
- The interface presents the following question:
"The slope of a vertical line is [Dropdown menu]. The equation of the vertical line passing through (7, 9) is [Text Box]."
- You should select "undefined" from the dropdown menu and enter "x = 7" in the text box.
By understanding these fundamental properties of vertical lines, one can easily determine both the slope and the corresponding equation for any given vertical line on a coordinate plane.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F04552051-e206-45f1-b504-e01aa8de9423%2F73e85ae2-6d73-4195-be4e-702b1a16e96b%2Flixq69b_processed.png&w=3840&q=75)
Transcribed Image Text:**Understanding Vertical Lines and Their Equations**
When dealing with vertical lines in a coordinate plane, there are specific characteristics and formulas that define them.
1. **The Slope of a Vertical Line:**
Vertical lines have a unique property where their slope is undefined. This is due to the fact that vertical lines rise infinitely without running horizontally, which causes the denominator in the slope formula (rise over run) to be zero, thus making the slope undefined.
In the provided interface, you will see a dropdown menu next to the text "The slope of a vertical line is". You need to select the appropriate term such as "undefined" from the dropdown in this scenario.
2. **The Equation of a Vertical Line:**
The equation of a vertical line is derived based on the constant x-value through which the line passes. For example, if a vertical line passes through the point (7, 9), the equation of the line is \( x = 7 \). This is because all points on this vertical line will have the same x-coordinate, which is 7.
In the provided interface, you will see a space next to the text "The equation of the vertical line passing through (7, 9) is". You should enter and confirm the equation \( x = 7 \) in this space.
**Example:**
- The interface presents the following question:
"The slope of a vertical line is [Dropdown menu]. The equation of the vertical line passing through (7, 9) is [Text Box]."
- You should select "undefined" from the dropdown menu and enter "x = 7" in the text box.
By understanding these fundamental properties of vertical lines, one can easily determine both the slope and the corresponding equation for any given vertical line on a coordinate plane.
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