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

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

Sagot :

GinnyAnsweridn
To determine the equation of the line that is parallel to the given line and passes through the specified point, let's analyze the given information.

1. The given line is \( x = -6 \). This is a vertical line because the equation is in the form \( x = \text{constant} \). Vertical lines always have the form \( x = k \), where \( k \) is a constant value.

2. A line that is parallel to \( x = -6 \) must also be a vertical line since parallel lines have the same orientation. Therefore, the equation of the parallel line will be in the form \( x = k \).

3. Now, we need to determine the specific value of \( k \) such that the line passes through the given point, \((-4, -6)\). The vertical line passing through any point has the equation \( x = \text{the x-coordinate of the point} \).

4. Here, the x-coordinate of the point \((-4, -6)\) is \(-4\).

Therefore, the equation of the line that is parallel to \( x = -6 \) and passes through the point \((-4, -6)\) is:
[tex]\[ x = -4 \][/tex]

Hence, the correct answer is:
[tex]\[ x = -4 \][/tex]
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