Perpendicular refers to the relationship between two lines or line segments that intersect at a right angle, forming a 90-degree angle. This concept is particularly important in the context of graphing linear equations, as perpendicular lines have significant geometric and algebraic properties.
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The slopes of two perpendicular lines are negative reciprocals of each other, meaning the product of their slopes is -1.
When graphing linear equations, perpendicular lines intersect at a single point, forming a 90-degree angle.
Perpendicular lines have the same x-intercept or y-intercept, depending on their orientation on the coordinate plane.
Perpendicular lines can be used to construct geometric shapes, such as squares and rectangles, on the coordinate plane.
The equation of a line perpendicular to another line can be found by negating the reciprocal of the original line's slope.
Review Questions
Explain the relationship between the slopes of two perpendicular lines.
The slopes of two perpendicular lines are negative reciprocals of each other. This means that if the slope of one line is $m$, the slope of the perpendicular line will be $-1/m$. This property is crucial when graphing linear equations, as it allows you to construct perpendicular lines by using the negative reciprocal of a given slope.
Describe how the orientation of perpendicular lines on the coordinate plane affects their intercepts.
The orientation of perpendicular lines on the coordinate plane determines which intercept they share. If two perpendicular lines are vertical and horizontal, they will share the same $x$-intercept. However, if the lines are not aligned with the coordinate axes, they will share the same $y$-intercept. This relationship between the intercepts of perpendicular lines is an important concept to understand when graphing linear equations and constructing geometric shapes on the coordinate plane.
How can the equation of a line perpendicular to another line be determined, and what is the significance of this relationship?
The equation of a line perpendicular to another line can be found by negating the reciprocal of the original line's slope. This means that if the slope of the original line is $m$, the slope of the perpendicular line will be $-1/m$. The significance of this relationship is that it allows you to construct perpendicular lines, which are essential for creating geometric shapes and understanding the properties of linear equations on the coordinate plane. Being able to determine the equation of a perpendicular line is a crucial skill for graphing and analyzing linear relationships.
The slope of a line represents the steepness or incline of the line, calculated as the change in y-coordinate divided by the change in x-coordinate between two points on the line.