What is the equation of the line that is parallel to the given line and passes through the point \((-4,-6)\)?

A. \(x = -6\)
B. \(x = -4\)
C. \(y = -6\)
D. [tex]\(y = -4\)[/tex]



Answer :

Sure! To find the equation of a line that is parallel to a given line and passes through a specific point, we need to first understand the properties of the given line.

1. Identify the given line: In this case, let's denote the given line as a vertical line. Vertical lines have an equation of the form \( x = c \), where \( c \) is the x-coordinate of any point on the line.

2. Understand parallel lines: For two lines to be parallel, their slopes must be identical. Vertical lines are parallel to each other because they both have undefined slopes. Hence, any line parallel to a vertical line will also be vertical.

3. Given point: The point through which the new line must pass is \((-4, -6)\).

4. Equation of parallel line: Since the line is vertical and must pass through the point \((-4, -6)\), the x-coordinate is always \(-4\).

Thus, the equation of the line that is parallel to the given vertical line and passes through the point \((-4, -6)\) is:

[tex]\[ x = -4 \][/tex]

Hence, the correct answer is:

[tex]\[ x = -4 \][/tex]