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ZingPath: Parallel Lines

Writing the Equations of Parallel and Perpendicular Lines

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Parallel Lines

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Lesson Focus

Writing the Equations of Parallel and Perpendicular Lines

Geometry

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You will find the equation of a line given a point on the line and the equation of a parallel or perpendicular line.

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Now You Know

After completing this tutorial, you will be able to complete the following:

  • Find the equation of a line given a point on the line and the equation of a parallel line.
  • Find the equation of a line given a point on the line and the equation of a perpendicular line.

Everything You'll Have Covered

The slopes of parallel or perpendicular lines are related in a way that offers both computational and conceptual tools. Computationally, the relationship helps to determine whether two lines are parallel, perpendicular, or neither. Conceptually, the relationship can help us to understand the concept of slope as a measure of steepness.

Two noncoincident lines in the plane are parallel just in case they do not intersect. In this context, noncoincident means that the lines do not completely overlap each other. Two lines in the plane are perpendicular if there is a right angle between them.

The conditions in the table can be verified by comparing the definition of slope to the definitions of parallelism and perpendicularity.

The relationship between the slopes of parallel or perpendicular lines can be used to write the equation of a line that is parallel or perpendicular to a given line passing through a specified point. A point is specified because there are infinitely many lines either parallel or perpendicular to some line, but only one that passes through a specific point. Consider the following example:

Tutorial Details

Approximate Time 20 Minutes
Pre-requisite Concepts Students should know the concepts of parallel and perpendicular lines, and how the slopes of parallel and perpendicular lines are related; how to find the slope of a line; and how to write the equation of a line in slope-intercept or point-slope form.
Course Geometry
Type of Tutorial Skills Application
Key Vocabulary parallel lines, perpendicular lines, point-slope form of an equation