What is the slope of a line that is perpendicular to [tex]y=7 x+12[/tex]?
Answer (1)
− 7 1
Explanation
Understanding the Problem The problem asks us to find the slope of a line that is perpendicular to the line given by the equation y = 7 x + 12 .
Identifying the Slope of the Given Line The equation y = 7 x + 12 is in slope-intercept form, which is y = m x + b , where m represents the slope of the line and b represents the y-intercept. In this case, the slope of the given line is m = 7 .
Understanding Perpendicular Slopes The slope of a line perpendicular to a given line is the negative reciprocal of the slope of the given line. If the slope of the given line is m , then the slope of the perpendicular line is − m 1 .
Calculating the Perpendicular Slope Since the slope of the given line is 7, the slope of the line perpendicular to it is − 7 1 .
Final Answer Therefore, the slope of a line perpendicular to y = 7 x + 12 is − 7 1 .
Examples
Understanding perpendicular slopes is crucial in many real-world applications, such as architecture and construction. When building structures, ensuring that walls are perpendicular to the ground is essential for stability. Similarly, in navigation, understanding perpendicular directions helps in plotting efficient routes. For example, if a road has a slope of 7, engineers need to know that a road perpendicular to it would have a slope of − 7 1 to design intersections correctly.
