To determine the equation of a line that is parallel to a given line and passes through a specific point, let's carefully analyze the given information.
1. Given Line Equation: The equation of the given line is [tex]\( x = 23 \)[/tex].
2. Nature of the Line: The equation [tex]\( x = 23 \)[/tex] represents a vertical line. Vertical lines have the same x-coordinate for all points on the line.
3. Parallel Line Characteristics: A line that is parallel to another line will have the same orientation. Therefore, a line parallel to the line [tex]\( x = 23 \)[/tex] will also be a vertical line. This means any line parallel to [tex]\( x = 23 \)[/tex] will have an equation in the form [tex]\( x = c \)[/tex], where [tex]\( c \)[/tex] is a constant.
4. Point Through Which the Parallel Line Passes: The point provided is [tex]\( (26, 22) \)[/tex]. Although the y-coordinate is given as 22, for a vertical line, the y-coordinate does not affect the equation since the x-coordinate determines the vertical line's location.
5. Equation of the Parallel Line: Since the line must pass through the point [tex]\( (26, 22) \)[/tex], the x-coordinate of this point is 26. Therefore, the equation of the vertical line passing through this point is:
[tex]\[
x = 26
\][/tex]
So, the equation of the parallel line that passes through the point [tex]\( (26, 22) \)[/tex] is [tex]\( x = 26 \)[/tex].
