Transcript 8.1 powerpoint for notes File

3-1
A-CED.A.2
Create
equations
in two or more variables to represent
Lines
and
Angles
relationships between quantities; graph equations on
coordinate axes with labels and scales.
A-CED.A.4
Rearrange formulas to highlight a quantity of interest,
using the same reasoning as in solving equations.

Combined variation

Inverse variation

Joint variation
Holt Geometry
3-1 Lines and Angles
 Paper for notes
 Pearson 8.1
 Graphing Calc.
Holt Geometry
TOPIC:
3-1 Lines
Name: Daisy Basset
and
Angles
Period:
8.1
Inverse
Variation
Objective:
Date :
Subject:
Notes
Rearrange formulas to
highlight a quantity of
interest, using the
same reasoning as in
solving equations.
Holt Geometry
3-1 Lines and Angles
Vocabulary
 Direct Variation
 Inverse Variation
Holt Geometry
3-1 Lines and Angles
1. Is the relationship
between the variables a
direct variation, an inverse
variation, or neither?
Write function models for
the direct and inverse
variations.
Holt Geometry
3-1 Lines and Angles
A.
x
2
4
10
15
y
15
7.5
3
2
xy
30
30
30
30
As x increases ,
y decreases .
It may vary inversely .
Test to see whether
xy is constant.
y varies inversely to x.
30
The function is y 
.
x
Holt Geometry
3-1 Lines and Angles
B.
x
2
4
10
15
As x increases ,
y decreases .
xy
20 It may vary inversely .
y
10
8 32
3 30 Test to see whether
1.5 22.5 xy is constant.
Since the products are not
constant, the relationship is
neither.
Holt Geometry
3-1 Lines and Angles
C.
x
y
0.2
0.5
1
1.5
8
20
40
60
As x increases ,
y
y increases .
x
40 It may vary directly .
40 Test to see whether
y
is constant.
40 .
40
x
y varies directly to x.
The function is y  40 x .
Holt Geometry
2.
Suppose x and y
vary inversely,
and x = 4 when
y = 12.
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
A. What function models
the inverse variation.
k
y
x
k
12 
4
Holt Geometry
3-1 Lines and Angles
k
12 
4
48  k
The function is
Holt Geometry
48
y
x
.
3-1 Lines and Angles
B.
What is y when x = 10?
48
y
x
48
y
10
y = 4.8 when x = 10.
Holt Geometry
3-1 Lines and Angles
 Notes 8.1 day
2
 Calculator
Holt Geometry
C.
Suppose x and y
vary inversely, and
x = 8 when y = -7.
What is the
function that
models the inverse
variation?
3-1 Lines and Angles
Holt Geometry
3-1 Lines and Angles
k
y
x
k
7 
8
56  k
 56
The function is y 
.
x
Holt Geometry
3-1 Lines and Angles
3. Each pair of
values is from a
direct variation.
Find the missing
value.
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(x, 12)(4, 1.5)
y = kx
3-1 Lines and Angles
1.5 = k4
1 .5
k
4
Holt Geometry
3-1 Lines and Angles
k  0.375
y = kx
(x, 12)
12 = 0.375x
x = 32
Holt Geometry
4. Each pair of
values is from a
inverse
variation.
Find the missing
value.
3-1 Lines and Angles
Holt Geometry
(x, 12)(4, 1.5)
3-1 Lines and Angles
k
y
x
k
1 .5 
4
1
k 6
Holt Geometry
(x, 12)
3-1 Lines and Angles
k
y
x
6
12 
x
Holt Geometry
k 6
3-1 Lines and Angles
6
12 
x
12x  6
6
1
x

12
2
Holt Geometry
3-1 Lines and Angles
 Notes 8.1
 Calculator
Holt Geometry
3-1 Lines and Angles
5. Your math class has
decided to pick up
litter each weekend in
a local park. Each
week there is
approximately the
same amount of litter.
Holt Geometry
3-1 Lines and Angles
The table shows the
number of students
who worked each of the
first four weeks of the
project and the time
needed for the pickup.
Holt Geometry
3-1 Lines and Angles
A.
# of students
(n)
Time in minutes
(t)
3
5
12
17
85
51
21
15
nt
255
255
252
255
The more students who help, the less
___
time the cleanup takes.
It may vary inversely.
Test to see whether nt is constant.
Holt Geometry
nt is almost always 255.
In real life data, 252 is
close enough.
Inverse variation is
still a good model.
3-1 Lines and Angles
255
The function is t 
.
n
Holt Geometry
3-1 Lines and Angles
B.How many students
should there be to
complete the
project in at most
30 minutes each
week?
Holt Geometry
Lines and Angles
3-1 255
t
n
255
30 
n
30n = 255
n = 8.5
9
There should be at least __
students to do the job in at
most 30 minutes.
Holt Geometry
3-1 Lines and Angles
Summary
D
L
I
Q
Holt Geometry
Summarize/reflect
What did I do?
What did I learn?
What did I find most
interesting?
What questions do I still
have? What do I need
clarified?
3-1 Lines and Angles
Hmwk 8.1 C
Math XL
Start Notes 8.2
Work on the Study Plan
Holt Geometry
3-1
8.2
The
Reciprocal
Function
Family
TOPIC: Lines and
Name: Angles
Daisy Basset
Period:
Objective:
Date :
Subject:
Notes
Identify the effect on the
graph of replacing f(x) by
f(x) + k and f(x+h) for
specific values of h and k
(both positive and negative).
Holt Geometry
3-1 Lines and Angles
Key Concepts
 General Form of
the Reciprocal
Function Family
 The Reciprocal
Function Family
Holt Geometry