Section 2.4
Parallel and Perpendicular Lines
1.Find the reciprocal of each fraction
a.
1
2
b.
4
3
c.
1

3
d.
5

2
2.Find the slope and y-intercept of each equation
5
a. y  x  4
4
5
b. y  x  8
3
c. y  6 x
d. y  6 x  2
Quick Review/Preview
1. What is the Slope-Intercept Form?
y = mx + b
2. What is the Standard Form?
Ax + By = C
3. What is the Point-Slope Form?
y – y1 = m(x – x1)
4. Find the “negative reciprocal” of each fraction
2
5
a.

5
2
3 7
b. 
7 3
1 2
4
c. 
 2 d. 
2 1
3
3
4
Overview
Parallel Lines and Perpendicular Lines
 Property of their slopes
 Write equations for each type of lines

Parallel Lines
Parallel Lines - lines that never intersect
What is the slope of the
red line?
1/2
What is the slope of the
blue line?
1/2
Parallel Lines have the same slope!
Parallel Lines
Determine if the lines are parallel
1
1. 2 x  6 y  12 and y   x  5
3
2x + 6y = 12
6y = -2x + 12
1
y  x2
3
yes
Parallel Lines
Determine if the lines are parallel
3
2. 6 x  8 y  24 and y 
x 3
4
6x + 8y = -24
8y = -6x – 24
3
y   x3
4
No
Parallel Lines
Determine if the lines are parallel
2
3. 4 x  6 y  2 and y  x  8
3
4x + 6y = -2
6y = -4x – 2
2
1
y  x
3
3
No
Equations of Parallel Lines
4. Write an equation for the line that
3
contains (5, 1) and is parallel to y  x  4
5
3
m=
5
3
y  1  x  5
5
Equations of Parallel Lines
5. Write an equation for the line that
contains (2, -6) and is parallel to y  3x  9
m=3
y + 6 = 3(x – 2)
Equations of Parallel Lines
6. Write an equation for the line that
1
contains (-4, 3) and is parallel to y  x  7
2
1
m=
2
1
y  3  x  4
2
Perpendicular Lines
Perpendicular Lines – lines that intersect to form
right angles
What is the slope of the
red line?
-1/4
What is the slope of the
blue line?
4/1
Perpendicular Lines have negative reciprocal slope!
Perpendicular Lines
What is the slope of the perpendicular line?
2
7. y  x  8
5
1
8. y   x
5
9. y  2 x  7
-5/2
5/1 = 5
1/2
Equations of Perpendicular Lines
10. Find the equation of the line that
contains (0, -2) and is perpendicular to
y = 5x + 3
1
m=
5
1
y2 x
5
Equations of Perpendicular Lines
11. Find the equation of the line that
contains (1, 8) and is perpendicular to
3
y  x 1
4
4
m =
3
4
y  8    x  1
3
Equations of Perpendicular Lines
12. Find the equation of the line that
contains (2, -3) and is perpendicular to
1
y   x6
2
m=2
y + 3 = 2(x – 2)
Perpendicular Lines
13. Determine if the lines are perpendicular:
2
y  x  1 and 3 y  2 x  4
3
3y  2x  4
3 y  2 x  4
2
4
y  x
3
3
No
14. Determine if the lines are perpendicular:
4
y  x  5 and 4 y  3 x  9
3
4y  3x  9
4 y  3 x  9
3
9
y  x
4
4
Yes
Challenge
What is the slope of the line that is parallel
to x = 4?
undefined
 What is the slope of the line that is
perpendicular to x = 4?
zero

The Average Rate of Change of
a Function
Let
(x1, f(x1)) and (x2, f(x2)) be distinct
points on the graph of a function f. The
average rate of change of f from x1 to x2 is
f ( x2 )  f ( x1 )
x2  x1
Example: Finding the Average
Rate of Change
Find
for
the average rate of change
f ( x)  x3 from x = –2 to x = 0.
1
2
f ( x2 )  f ( x1 )
x2  x1
f (0)  f (2) (0)3  (2)3
8



4
0  (2)
2
2