1. 6-6 Parallel and Perpendicular Lines

2. (one is the opposite reciprocal of the other)
Slopes of Lines
Parallel lines have equal slopes but different y- intercepts.
Perpendicular lines have slopes that multiply to get -1.
(one is the opposite reciprocal of the other)

3. How to Tell
Get both equations into slope-intercept form and compare slopes.
If slopes are equal, check the y-intercepts.

4. slope = 2, parallel slope = 2, through (4,1)
Example #1
Write an equation for a line parallel to y – 2x = 3 that goes through (4,1).
y – 2x = 3
+2x +2x
y = 2x +3
slope = 2, parallel slope = 2, through (4,1)
y – y1 = m (x – x1)

5. slope = 2, parallel slope = 2, through (4,1)
Example
Write an equation for a line parallel to y – 2x = 3 that goes through (4,1).
y – 2x = 3
+2x +2x
y = 2x +3
slope = 2, parallel slope = 2, through (4,1)
y – y1 = m (x – 4)

6. slope = 2, parallel slope = 2, through (4,1)
Example
Write an equation for a line parallel to y – 2x = 3 that goes through (4,1).
y – 2x = 3
+2x +2x
y = 2x +3
slope = 2, parallel slope = 2, through (4,1)
y – 1 = m (x – 4)

7. slope = 2, parallel slope = 2, through (4,1)
Example
Write an equation for a line parallel to y – 2x = 3 that goes through (4,1).
y – 2x = 3
+2x +2x
y = 2x +3
slope = 2, parallel slope = 2, through (4,1)
y – 1 = 2 (x – 4)

8. slope = 2, perpendicular slope = -½, through (4,1)
Example #2
Write an equation for a line perpendicular to y – 2x = 3 that goes through (4,1).
y – 2x = 3
+2x +2x
y = 2x +3
slope = 2, perpendicular slope = -½, through (4,1)
y – 1 = -½ (x – 4)

9. Today’s Assignment
p. 346 #1-29 odd, all