Transcript 3.8 Slopes of Parallel and Perpendicular Lines

3.8 Slopes of Parallel and Perpendicular Lines
• Slopes of Parallel Lines
– If two nonvertical lines are parallel, then their slopes
are equal.
– If the slopes of two distinct nonvertical lines are
equal, then the lines are parallel.
– Any two vertical lines or horizontal lines are parallel.
Checking for Parallel Lines
• Are lines ℓ1 and ℓ2 parallel? Explain.
Checking for Parallel Lines
• Find the slope of each line.
y2  y1 5  ( 4)
9
m1 


 3
x2  x1
1  2
3
y2  y1 3  (4)
7
7
m2 



x2  x1 3  (1) 2
2
7
3  
NOT
2 PARALLEL!!!!!!
Writing Equations of Parallel Lines
• What is an equation of the line parallel to
y = -3x – 5 that contains (-1 , 8)?
y = -3x – 5
parallel slope = -3
y – y1 = m (x – x1)
y – 8 = -3 (x + 1)
Slopes of Perpendicular Lines
• If two nonvertical lines are perpendicular,
then the product of their slopes is -1
(opposite reciprocal).
• If the slopes of two lines have a product of
-1, then the lines are perpendicular.
• Any horizontal line and vertical line are
perpendicular.
Checking for Perpendicular Lines
• Lines ℓ1 and ℓ2 are neither horizontal nor vertical. Are
they perpendicular? Explain.
Checking for Perpendicular Lines
• Find the slope of each line.
y2  y1 2  ( 4) 6
3
m1 



x2  x1
4  0
2
4
y2  y1 3  (3)
6
m2 


x2  x1 4  (5)
9
2

3
Perpendicular. The slopes have a
product of -1.
Writing Equations of Perpendicular Lines
• What is an equation of the line perpendicular to
1
y  x  2 that contains (15 , -4)?
5
m  5
y  y1  m( x  x1 )
y  4  5( x  15)
More Practice!!!!!
• Homework – Textbook p. 201 – 202 #8 –
20 even.