Select The Correct Answer.Which Equation Represents The Vertical Line Passing Through \[$(1,-9)\$\]?A. \[$x = -9\$\] B. \[$x = 1\$\] C. \[$y = -9\$\] D. \[$y = 1\$\]

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Introduction

In mathematics, a vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis. It is represented by an equation in the form of x = a, where 'a' is a constant value. In this article, we will discuss how to select the correct equation that represents a vertical line passing through a given point.

What is a Vertical Line?

A vertical line is a line that has a constant x-coordinate value. It is perpendicular to the horizontal lines, which have a constant y-coordinate value. The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.

Equation of a Vertical Line

The equation of a vertical line is given by x = a, where 'a' is the x-coordinate value of the point through which the line passes. For example, if the vertical line passes through the point (3, 4), the equation of the line will be x = 3.

Selecting the Correct Equation

Now, let's consider the given options and select the correct equation that represents the vertical line passing through the point (1, -9).

Option A: x = -9

This equation represents a vertical line passing through the point (-9, 0). However, the given point is (1, -9), which is not on the line x = -9.

Option B: x = 1

This equation represents a vertical line passing through the point (1, 0). However, the given point is (1, -9), which is not on the line x = 1. But, the x-coordinate of the given point is 1, so this option is a strong candidate.

Option C: y = -9

This equation represents a horizontal line passing through the point (0, -9). However, the given point is (1, -9), which is not on the line y = -9.

Option D: y = 1

This equation represents a horizontal line passing through the point (0, 1). However, the given point is (1, -9), which is not on the line y = 1.

Conclusion

Based on the analysis of the given options, the correct equation that represents the vertical line passing through the point (1, -9) is x = 1. This equation represents a vertical line that passes through the point (1, -9).

Key Takeaways

  • A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis.
  • The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.
  • To select the correct equation, we need to analyze the given options and identify the equation that represents a vertical line passing through the given point.

Frequently Asked Questions

Q: What is a vertical line?

A: A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis.

Q: What is the equation of a vertical line?

A: The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.

Q: How to select the correct equation?

A: To select the correct equation, we need to analyze the given options and identify the equation that represents a vertical line passing through the given point.

References

Introduction

In our previous article, we discussed the concept of vertical lines in mathematics and how to select the correct equation that represents a vertical line passing through a given point. In this article, we will provide a Q&A section to help you better understand the concept of vertical lines and how to apply it in different mathematical scenarios.

Q&A Section

Q: What is a vertical line?

A: A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis.

Q: What is the equation of a vertical line?

A: The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.

Q: How to select the correct equation for a vertical line?

A: To select the correct equation, you need to analyze the given options and identify the equation that represents a vertical line passing through the given point. In the case of the point (1, -9), the correct equation is x = 1.

Q: What is the difference between a vertical line and a horizontal line?

A: A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis, while a horizontal line is a line that extends infinitely in the horizontal direction, parallel to the x-axis.

Q: How to graph a vertical line?

A: To graph a vertical line, you need to plot a point on the coordinate plane and draw a line that extends infinitely in the vertical direction, parallel to the y-axis.

Q: What is the significance of vertical lines in mathematics?

A: Vertical lines play a crucial role in mathematics, particularly in geometry and algebra. They are used to represent relationships between variables and to solve equations.

Q: Can a vertical line have a slope?

A: No, a vertical line cannot have a slope. The slope of a line is a measure of how steep it is, and a vertical line is perpendicular to the x-axis, so it has no slope.

Q: How to find the equation of a vertical line that passes through a given point?

A: To find the equation of a vertical line that passes through a given point, you need to identify the x-coordinate value of the point and use it as the value of 'a' in the equation x = a.

Q: Can a vertical line be parallel to a horizontal line?

A: Yes, a vertical line can be parallel to a horizontal line. In fact, all vertical lines are parallel to each other, and all horizontal lines are parallel to each other.

Q: How to determine if two lines are parallel?

A: To determine if two lines are parallel, you need to check if they have the same slope or if they are perpendicular to each other.

Conclusion

In this Q&A article, we have provided answers to some of the most frequently asked questions about vertical lines in mathematics. We hope that this article has helped you better understand the concept of vertical lines and how to apply it in different mathematical scenarios.

Key Takeaways

  • A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis.
  • The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.
  • To select the correct equation, you need to analyze the given options and identify the equation that represents a vertical line passing through the given point.
  • Vertical lines play a crucial role in mathematics, particularly in geometry and algebra.

Frequently Asked Questions

Q: What is a vertical line?

A: A vertical line is a line that extends infinitely in the vertical direction, parallel to the y-axis.

Q: What is the equation of a vertical line?

A: The equation of a vertical line is in the form of x = a, where 'a' is the x-coordinate value of the point through which the line passes.

Q: How to select the correct equation?

A: To select the correct equation, you need to analyze the given options and identify the equation that represents a vertical line passing through the given point.

References