What is the slope of a line that is perpendicular to the line [tex]y=8x-8[/tex]?
Answer (2)
Identify the slope of the given line as 8.
Calculate the negative reciprocal of the slope.
The slope of the perpendicular line is − 8 1 .
The final answer is − 8 1 .
Explanation
Identify the slope of the given line The given line is in slope-intercept form, y = m x + b , where m represents the slope and b represents the y-intercept. In the equation y = 8 x − 8 , the slope of the given line is 8.
Understanding perpendicular slopes The slope of a line perpendicular to a given line is the negative reciprocal of the given line's slope. If the slope of the given line is m , then the slope of the perpendicular line is − m 1 .
Calculate the negative reciprocal Since the slope of the given line is 8, the slope of the perpendicular line is − 8 1 .
Examples
Understanding perpendicular slopes is crucial in various real-world applications, such as designing roads and buildings. For example, when constructing a ramp that needs to be perpendicular to a wall, knowing the slope of the wall and calculating the negative reciprocal will ensure the ramp is correctly aligned. In architecture, ensuring walls are perpendicular to the ground involves similar slope calculations. If a wall has a slope represented by the equation y = m x + c , a line perpendicular to it will have a slope of − m 1 . This principle helps architects and engineers maintain structural integrity and proper alignment in their designs.
The slope of the given line is 8. The slope of a line that is perpendicular to it is the negative reciprocal, which equals − 8 1 . Thus, the answer is − 8 1 .
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