Notes for Lesson 5-6: Slopes of Parallel and Perpendicular lines
5-6.1 – Identifying Parallel lines
Vocabulary:
Parallel lines – lines in the same plane that do not intersect
You can identify parallel lines by their slopes. If their slopes are the same, than the lines will be parallel. So first, write the equation of the line in a way you can recognize the slope. Then compare the slopes to see if they are the same.
Examples:
Identify which lines are parallel:
The slopes are: The slopes are:
So, So,
andand
5-6.2 – Identifying Perpendicular lines
Vocabulary:
Perpendicular lines – lines that intersect to form right angles
Opposite Reciprocals – two numbers whose product is -1
You can identify lines that would be perpendicular to each other by their slopes as well. If the two slopes have a product of -1 then the lines will form 90 degree angles.
Examples: Identify which lines are perpendicular
The slopes are: The slopes are
So the lines are perpendicular and so areSo the lines are
and so are
5-6.3 – Writing a line parallel to a given line through a given point
You can write a line parallel to a given line by using the same slope as the original line. Then write a line using the slope and point as we did earlier in Chapter 5.
Examples:
Write an equation in slope-intercept form for the line that passes through (4,5) and is parallel to the line
The slope of the given line is 5
So,
Write an equation in slope-intercept form parallel to and passes through (5,7)
The slope of the line is
So,
Write an equation in slope-intercept form parallel to and passes through (4,-3)
The slope of the line is
So,
5-6.4 – Writing a line perpendicular to a given line through a given point
You can write a line perpendicular to a given line by using the opposite reciprocal as the slope. Then write a line using the slope and point as we did earlier in Chapter 5.
Write an equation in slope-intercept form for the line that passes through (3,2) and is perpendicular to the line
The slope is 3 so the perpendicular slope is
So,
Write the equation in slope-intercept form of the line perpendicular to and passes through (-5,3)
The slope is 5 so the perpendicular slope is
So,
Write the equation in slope-intercept form of the line perpendicular to and passes through (4,5)
The slope is so the perpendicular slope is 4
So,