Geometry Section 3.6“Slope of Parallel and Perpendicular

lines”

 Recall how to find the slope of a line through two points (x1, y1) and (x2, y2).  

m = 12

12

xx

yy

When working with the graph of a line, you may prefer to think of slope as ____________ runover rise

 Example: Find the slope of the line through each pair of points. 1. (-2, -3) (5, 7) 2. (-3, 2) (4, -6)

3. (5, -4) (5, 6) 4. (8, -1) (13, -1)

7

10

25

37

7

8

34

26

0

10

55

46

undefined5

0

813

11

0

If the slope of a line is positive, then __________________________

If the slope of a line is negative, then __________________________

If the slope of a line is zero, then ____________________

If the slope of a line is undefined, then ____________________

right left to from rises line the

right left to from falls line the

horizontal is line the

verticalis line the

Example: Find y so that the slope of the line

through the points (5, y) and (-3, 4) is 2

3

35

4

y

2

3

8

4

y

8

162

2482

y

y

y

24)4(2 y

Two nonvertical lines are parallel if __________________

Note: Vertical lines are parallel, but since their slopes are undefined, we can’t say the slopes are equal.

equal are slopestheir

Two lines, neither of which is vertical, are perpendicular if ________________________________sreciprocal opposite are slopestheir

signs

of change

fraction

theflip

Example: Give the slope of a line parallel to a line with the given slope and give the slope of a line perpendicular to a line with the given slope.

5

39

4 2 0

3

54

92

1 undefined