What is the slope of a line that is perpendicular to the line [tex]$x=-3$[/tex]?
Answer (2)
Recognize that the line x = − 3 is a vertical line.
Recall that a line perpendicular to a vertical line is a horizontal line.
Recall that the slope of a horizontal line is 0.
Therefore, the slope of a line perpendicular to x = − 3 is 0 .
Explanation
Analyze the given line The given line is x = − 3 . This is a vertical line. We need to find the slope of a line that is perpendicular to this vertical line.
Determine the perpendicular line type A line perpendicular to a vertical line is a horizontal line.
State the slope of the perpendicular line The slope of a horizontal line is 0. Therefore, the slope of a line perpendicular to x = − 3 is 0.
Examples
Imagine you're drawing lines on a graph. If you draw a straight vertical line, like the side of a tall building, any line that forms a perfect 'L' shape with it (a right angle) must be perfectly flat, like the ground. That flat line has a slope of zero, meaning it doesn't go up or down at all. This concept is used in construction to ensure walls are perfectly vertical and floors are perfectly horizontal.
The slope of a line that is perpendicular to the line given by x = − 3 is 0 . This is because x = − 3 is a vertical line, and a perpendicular line to it must be horizontal, which has a slope of zero. Therefore, the answer is 0 .
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