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Parallel Lines and Perpendicular Lines




 
Related Topics: More geometry Lessons, Coordinate geometry games

In these lessons, we will learn
  • how to determine if two lines are parallel when given their slopes.
  • how to determine if two lines are perpendicular when given their slopes.
  • how to find the equation of a line given a point on the line and a line that is parallel to it.
  • how to find the equation of a line given a point on the line and a line that is perpendicular to it.
  • how to find parallel lines using Standard Form
  • how to find perpendicular lines using Standard Form

Slopes Of Parallel Lines

In Coordinate Geometry, two lines are parallel if their slopes (m) are equal.

    parallel lines

For example: The line line equation is parallel to the line. line equation Their slopes are both the same.

In the Coordinate Plane, two lines are perpendicular if the product of their slopes (m) is –1. The slopes are negative reciprocals of each other.

perpendicular

For example: The line line equation is perpendicular to the line y = –2x – 1. The product of the two slopes is 1/2 * -2




The following video shows how we can determine whether a given pair of lines are parallel or perpendicular.

Equation of a line given a point on the line and a line that is parallel to it

The following video shows how write the equation of a line given a point on the line and a line that is parallel to it.


 
This video involves equations of lines that are parallel or perpendicular to a given line, using slope-intercept (y = mx + b) form.
How to find the equation of a line given a point on the line and a line that is parallel to it.
How to find the equation of a line given a point on the line and a line that is perpendicular to it.

Equation of a line given a point on the line and a line that is perpendicular to it.

The following video gives an example of how to find the equation of a line given a point on the line and a line that is perpendicular to it.


Find Parallel Lines using Standard Form

Another method to find the equation of a parallel line would be to use the Standard Form of the equation.

The following video shows how to find parallel lines using Standard Form.

Find Perpendicular Lines using Standard Form

Another method to find the equation of a perpendicular line would be to use the Standard Form of the equation.

The following video shows how to find perpendicular lines using Standard Form.


 

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.


You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.


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