3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1) To relate slope and parallel lines.
2) To relate slope and perpendicular lines.
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Key Concepts
The relationship between slope and parallel lines is summarized below:
Summary
Slopes of Parallel Lines
If two nonvertical lines are parallel, their slopes are equal.
If the slopes of two distinct nonvertical lines are equal, the lines are parallel.
Any two vertical lines are parallel.
Summary
Slopes of Perpendicular Lines
If two nonvertical lines are perpendicular, the product of their slopes is -1.
If the slopes of two lines have a product of -1, the lines are perpendicular.
Any horizontal line and vertical line are perpendicular.
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Determine Whether Lines Are Parallel
Are the lines y =  5x + 4 and x =  5y + 4 parallel? Explain.
(Process: Write both equations in slope intercept form and compare slopes.)
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Writing Equations of Parallel Lines
Write an equation in point-slope form for the line parallel to 6x 3y = 9 that contains (5,8).
Step 1: To find the slope of the line, rewrite the equation in slope-intercept form:
6x
3
6x
2x
3
3
2
Step 2: Use slope-intercept form to write an equation for the new line.
y1
m
8
8
x1
5
2
2
5
2
(5,8)
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
1. Are the lines parallel? Explain.
a. y = x + 5 and 2x + 4y = 9
b. y = x + 5 and 2x + 4y = 20
 Show the work:
 Show the work:
2. Write an equation for the line parallel to y = -x + 4 that contains (-2, 5).
 Show the work:
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Writing Equations for Perpendicular Lines
Write an equation for a line perpendicular to 5x + 2y = 1 that contains (10, 0).
Step 1: To find the slope of the given line, rewrite the equation in slope-intercept form.
Step 2 Find the slope of a line perpendicular to 5x +2y = 1. Let m be the slope of the perpendicular line.
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Write an equation for the line perpendicular to 5y - x = 10 that contains (15,-4).
 Show the work:
3-7 Slopes of Parallel & Perpendicular Lines
Objectives:
1. To relate slope and parallel lines.
2. To relate slope and perpendicular lines.
Go to PRACTICE 3–7
page 305
Working on all odd numbers only.