Answer :
To determine which equation represents the vertical line passing through the point [tex]\((7, -3)\)[/tex], let's break down the problem step-by-step.
1. Understanding Vertical Lines:
- A vertical line is defined as a line where all points on the line have the same x-coordinate.
- Because all points on this line share the same x-coordinate, the equation of a vertical line is of the form [tex]\(x = a\)[/tex], where [tex]\(a\)[/tex] is the x-coordinate of any point on the line.
2. Analyzing the Given Point:
- The point provided is [tex]\((7, -3)\)[/tex]. This point gives us specific coordinates where [tex]\(x = 7\)[/tex] and [tex]\(y = -3\)[/tex].
3. Determining the Equation:
- Since the line is vertical and intersects the x-axis at [tex]\(x = 7\)[/tex], the equation of the line must be [tex]\(x = 7\)[/tex].
4. Verifying the Correct Option:
- The options given are:
- A. [tex]\(x = -3\)[/tex]
- B. [tex]\(y = -3\)[/tex]
- C. [tex]\(x = 7\)[/tex]
- D. [tex]\(y = 7\)[/tex]
- From the above analysis, we know that the correct equation for the vertical line passing through [tex]\((7, -3)\)[/tex] is [tex]\(x = 7\)[/tex].
Therefore, the correct answer is:
C. [tex]\(x = 7\)[/tex]
1. Understanding Vertical Lines:
- A vertical line is defined as a line where all points on the line have the same x-coordinate.
- Because all points on this line share the same x-coordinate, the equation of a vertical line is of the form [tex]\(x = a\)[/tex], where [tex]\(a\)[/tex] is the x-coordinate of any point on the line.
2. Analyzing the Given Point:
- The point provided is [tex]\((7, -3)\)[/tex]. This point gives us specific coordinates where [tex]\(x = 7\)[/tex] and [tex]\(y = -3\)[/tex].
3. Determining the Equation:
- Since the line is vertical and intersects the x-axis at [tex]\(x = 7\)[/tex], the equation of the line must be [tex]\(x = 7\)[/tex].
4. Verifying the Correct Option:
- The options given are:
- A. [tex]\(x = -3\)[/tex]
- B. [tex]\(y = -3\)[/tex]
- C. [tex]\(x = 7\)[/tex]
- D. [tex]\(y = 7\)[/tex]
- From the above analysis, we know that the correct equation for the vertical line passing through [tex]\((7, -3)\)[/tex] is [tex]\(x = 7\)[/tex].
Therefore, the correct answer is:
C. [tex]\(x = 7\)[/tex]
