What is the slope of a line that is perpendicular to the line [tex]$y=1$[/tex]?
Answer (2)
The line y = 1 is a horizontal line.
A line perpendicular to a horizontal line is a vertical line.
The slope of a vertical line is undefined.
Therefore, the slope of a line perpendicular to y = 1 is undefined .
Explanation
Analyze the problem The given line is y = 1 . This is a horizontal line. We need to find the slope of a line that is perpendicular to this horizontal line.
Determine the type of perpendicular line A line perpendicular to a horizontal line is a vertical line.
State the slope of a vertical line The slope of a vertical line is undefined.
Conclusion Therefore, the slope of a line perpendicular to the line y = 1 is undefined.
Examples
In architecture, understanding perpendicular lines is crucial for designing stable structures. For example, a horizontal floor (like the line y = 1 ) must be supported by vertical columns. Since vertical lines have an undefined slope, this concept helps architects ensure that supporting structures are perfectly upright, providing maximum stability and safety to the building.
The slope of a line perpendicular to y = 1 is undefined because y = 1 is a horizontal line, and perpendicular lines to horizontal lines are vertical. Vertical lines have an undefined slope.
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