Wize High School Geometry Textbook (Common Core) > Lines
Equations of Parallel & Perpendicular Lines
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Parallel & Perpendicular Lines
When we are given the equation of two lines, we can determine if the lines are parallel or perpendicular by looking at the slopes of the lines.
Parallel Lines
Two lines are parallel if they have the same slope.
(If two lines have the same slope, then they are parallel)
Example
Show that the lines and are parallel.
The line has a slope .
Rearranging the line into slope y-intercept form:
We see that this line also has a slope of .
Therefore, the lines are parallel.
Perpendicular Lines
Two lines are perpendicular if their slopes are negative reciprocals of one another.
(If two lines have negative reciprocal slopes, then they are perpendicular)
Wize Tip
The negative reciprocal of a number is just the "negative flip" of that number.
Examples
- and are negative reciprocals of one another
- and are negative reciprocals of one another
- and are negative reciprocals of one another
Example
Write the equation of a line that is perpendicular to .
The slope of the line is . The negative reciprocal of this number is .
So, any line that perpendicular to must have a slope of . One example would by .
There are many possible answers because there are many lines that are perpendicular to , we just have to change the y-intercept value and we have another line that is perpendicular to the given line.
Practice: Parallel Lines
Select all of the lines that are parallel to
Practice: Perpendicular Lines
Match the lines that are perpendicular to each other.
A.
B.
C.
D.
E.
Practice: Finding Equations of Lines
Determine the equation of each line based on the information given.
a) The line that passes through the point and is parallel to the line .
b) The line that passes through the point and is perpendicular to the line .