8-1: Slopes of Parallel and Perpendicular Lines Objectives: Assignment:

8-1: Slopes of Parallel and Perpendicular Lines
Objectives:
1. To find the slopes of
parallel and
perpendicular lines
Assignment:
• P. 91: 8-12
• P. 97: 1-10
• Challenge Problems
Ramp 1
Exercise 1
How would you
describe the roof at
the right?
Rate of Change
A rate of change is how much one
quantity changes (on average) relative
to another.
Slope can be used to represent an
average rate of change.
For slope, we measure how 𝑦
changes relative to 𝑥.
Exercise 2
The slope or pitch of
a roof is quite a
useful
measurement.
How do you think a
contractor would
measure the slope
or pitch of a roof?
Exercise 2
The slope or pitch of
a roof is defined as
the number of
vertical inches of
rise for every 12
inches of horizontal
run.
Exercise 2
The steeper the roof,
the better it looks,
and the longer it
lasts. But the cost
is higher because
of the increase in
the amount of
building materials.
Investigation 1
Use the Geometer’s
Sketchpad activity to
discover something
about the actual value
of the slope of a line.
Then complete the
table on the next
slide.
Slope Summary
Summarize your findings about slope in the
table below:
m>0
m<0
m=0
m = undef
Insert
Picture
Insert
Picture
Insert
Picture
Insert
Picture
As the absolute value of the slope of a line
the line gets steeper.
increases, --?--.
Slope of a Line
The slope m of a
nonvertical line is
the ratio of vertical
change (the ryse)
to the horizontal
change (the run).
ryse
ryse
Ramp 2
Parallel and Perpendicular
Two lines are
parallel lines iff
they have the
same slope.
Two lines are
perpendicular lines
iff their slopes are
negative reciprocals.
Exercise 3
Line k passes through
(0, 3) and (5, 2).
Graph the line
perpendicular to k
that passes through
point (1, 2).
Exercise 4
Find the value of y so that the line passing
through the points (3, y) and (−5, −6) is
perpendicular to the line that passes
through the points (−2, −7) and (10, 1).
Exercise 5
Find the value of k so that the line through
the points (k – 3, k + 2) and (2, 1) is parallel
to the line through the points (−1, 1) and
(3, 9).
8-1: Slopes of Parallel and Perpendicular Lines
Objectives:
1. To find the slopes of
parallel and
perpendicular lines
Assignment:
• P. 91: 8-12
• P. 97: 1-10
• Challenge Problems