Reteach 4-5 Scatter Plots and Trend Lines - Amazon S3

Name Date Class

LESSON Reteach
4-5 Scatter Plots and Trend Lines

Correlation is one way to describe the relationship between two sets of data.

Y

Positive Correlation
Data: As one set increases, the other set increases.
Graph: The graph goes up from left to right.

Negative Correlation 0OSITIVE X
Data: As one set increases, the other set decreases.
Graph: The graph goes down from left to right. Y

No Correlation .EGATIVE X
Data: There is no relationship between the sets.
Graph: The graph has no pattern. Y

.O X

Identify the correlation you would expect to see between the number
of grams of fat and the number of calories in different kinds of pizzas.

When you increase the amount of fat in a food, you also increase calories.
So you would expect to see a positive correlation.

Identify the correlation you would expect to see between
each pair of data sets. Explain.

1. the number of knots tied in a rope and the length of the rope

Negative correlation; each knot decreases the length of the rope

2. the height of a woman and her score on an algebra test

No correlation; there is no relationship between height and algebra skill

Describe the correlation illustrated by each scatter plot.

3. Y 4. Y




0ERCENT

Name Date Class

LESSON Reteach
4-5 Scatter Plots and Trend Lines (continued)

By drawing a trend line over a graph of data, you can make predictions.

The scatter plot shows a relationship between a man’s height and
the length of his femur (thigh bone). Based on this relationship,
predict the length of a man’s femur if his height is 160 cm.

Step 1: Draw a trend line through the points. Y Your line should have about as

Step 2: Go from 160 cm on the x-axis up to many points above it as below
the line. it. It may or may not pass

Step 3: Go from the line left to the y-axis. through some points.

The point (160, 41) is on the line. &EMUR

LESSON Scatter Plots and Trend Lines
4-5

Lesson Objectives
Create and interpret scatter plots; Use trend lines to make predictions

Vocabulary
scatter plot (p. 262): ________________________________________________
________________________________________________________________
correlation (p. 262): ________________________________________________
________________________________________________________________
positive correlation (p. 263): __________________________________________
________________________________________________________________
negative correlation (p. 263): _________________________________________
________________________________________________________________
no correlation (p. 263): ______________________________________________
________________________________________________________________
trend line (p. 265): _________________________________________________
________________________________________________________________

Copyright © by Holt, Rinehart and Winston. 6 43 Algebra 1
All rights reserved.

LESSON 4-5 CONTINUED Correlations No Correlation
Negative Correlation
Key Concepts
Correlations (p. 263):

Positive Correlation

Think and Discuss (p. 265)

Get Organized Complete the graphic organizer with either a scatter plot, or a
real-world example, or both.

GRAPH EXAMPLE

Positive
Correlation

Negative
Correlation

No
Correlation

Copyright © by Holt, Rinehart and Winston. 645 Algebra 1
All rights reserved.

Name Date Class

LESSON Practice A .UMBER

E X P L O R AT I O N

{‡È ÀˆÌ…“ïVÊ-iµÕi˜ViÃ

-EI

Name Date Class

LESSON Reteach
4-6 Arithmetic Sequences

An arithmetic sequence is a list of numbers (or terms) with a common difference between
each number. After you find the common difference, you can use it to continue the sequence.

Determine whether each sequence is an arithmetic
sequence. If so, find the common difference and the next three terms.

1, 2, 4, 8,... Find how much you add or subtract
ϩ1 ϩ2 ϩ4 to move from term to term.

The difference between terms is not constant.

This sequence is not an arithmetic sequence.

0, 6, 12, 18, ... Find how much you add or subtract
ϩ6 ϩ6 ϩ6 to move from term to term.

The difference between terms is constant.

This sequence is an arithmetic sequence with a common difference of 6.

0, 6, 12, 18, 24, 30, 36 Use the difference of 6
ϩ6 ϩ6 ϩ6 to find three more terms.

Fill in the blanks with the differences between terms. State whether
each sequence is an arithmetic sequence.

1. 14, 12, 10, 8, ... Is this an arithmetic sequence? yes
no
–2, –2, –2

2. 0.3, 0.6, 1.0, 1.5, ... Is this an arithmetic sequence?

ϩ0.3, ϩ0.4, ϩ0.5

Use the common difference to find the next three terms in each

arithmetic sequence.

3. 7, 4, 1, Ϫ2, –5 , –8 , –11, ... 4. Ϫ5, 0, 5, 10, 15 , 20 , 25 , ...

Ϫ3 Ϫ3 Ϫ3 Ϫ3 Ϫ3 Ϫ3 ϩ5 ϩ5 ϩ5

Determine whether each sequence is an arithmetic sequence. If so,
find the common difference and the next three terms.

5. Ϫ1, 2, Ϫ3, 4, ...

no

6. 1.25, 3.75, 6.25, 8.75, ...

yes; 2.5; 11.25, 13.75, 16.25

Copyright © by Holt, Rinehart and Winston. 467 Holt Algebra 1
All rights reserved.

Name Date Class

LESSON Reteach
4-6 Arithmetic Sequences (continued)

You can use the first term and common difference of an arithmetic sequence to write a rule in

this form: an ϭ a1 ϩ ͑n Ϫ 1 ͒d

any term first term term number common difference

After you write the rule, you can use it to find any term in the sequence.

Find the 50th term of this arithmetic sequence:

5, 3.8, 2.6, 1.4, ... The first term is 5.
Ϫ1.2 Ϫ1.2 Ϫ1.2

The common difference is –1.2.

First, write the rule.

an ϭ a1 ϩ ͑n Ϫ 1 ͒d Write the general form for the rule.

an ϭ 5 ϩ ͑n Ϫ 1 ͒ ͑Ϫ1.2 ͒ Substitute the first term and common difference.

Now, use the rule to find the 50th term.

a50 ϭ 5 ϩ ͑50 Ϫ 1 ͒ ͑Ϫ1.2 ͒ Substitute the term number.
a50 ϭ 5 ϩ ͑49 ͒ ͑Ϫ1.2 ͒ Simplify.
a50 ϭ 5 ϩ ͑Ϫ58.8 ͒
a50 ϭ Ϫ53.8
The 50th term is Ϫ53.8.

Use the first term and common difference to write the rule for each
arithmetic sequence.

7. The arithmetic sequence with first term an ϭ 10 ϩ ͑n Ϫ 1 ͒ ͑4 ͒
a1 ϭ 10 and common difference d ϭ 4. an ϭ Ϫ5 ϩ ͑n Ϫ 1 ͒ ͑5 ͒

8. Ϫ5, 0, 5, 10, ... –5
first term: a1 ϭ
5
common difference: d ϭ

Find the indicated term of each arithmetic sequence. 15th term: 9
9. an ϭ 16 ϩ ͑n Ϫ 1 ͒ ͑Ϫ0.5 ͒

10. an ϭ 6 ϩ ͑n Ϫ 1 ͒ ͑3 ͒ 32nd term: 99

11. Ϫ8, Ϫ6, Ϫ4, Ϫ2, ... 100th term: 190

Copyright © by Holt, Rinehart and Winston. 478 Holt Algebra 1
All rights reserved.

LESSON Arithmetic Sequences
4-6

Lesson Objectives
Recognize and extend an arithmetic sequence; Find a given term of an arithmetic
sequence

Vocabulary
sequence (p. 272): _________________________________________________
________________________________________________________________
term (p. 272): _____________________________________________________
________________________________________________________________
arithmetic sequence (p. 272):_________________________________________
________________________________________________________________
common difference (p. 272):__________________________________________
________________________________________________________________

Key Concepts
Finding the nth Term of an Arithmetic Sequence (p. 273):

Finding the nth Term of an Arithmetic Sequence

Think and Discuss (p. 274)

Get Organized Complete the graphic organizer with steps for finding the nth
term of an arithmetic sequence.

Finding the n th Term of an 1. 2.
Arithmetic Sequence

Copyright © by Holt, Rinehart and Winston. 696 Algebra 1
All rights reserved.

Name Date Class

LESSON Practice A
4-6 Arithmetic Sequences

Determine if the sequence is arithmetic. Write yes or no. arithmetic sequence: pattern
with common differences
1. 5, 9, 14, 20, … 2. 10, 22, 34, 46, …

no yes

Find the common difference for each arithmetic sequence. common difference:
same difference from
3. 12, 15, 18, 21, … 4. 30, 24, 18, 12, … one term to the next

3 Ϫ6

Find the common difference for each arithmetic sequence. Then find
the next three terms.

5. 20, 10, 0, Ϫ10, … 6. 100, 98, 96, 94, …

d ϭ Ϫ10; Ϫ20, Ϫ30, Ϫ40 d ϭ Ϫ2; 92, 90, 88

Find the requested term for each arithmetic sequence.

7. 42nd term: a1 ϭ 10; d ϭ 6 8. 27th term: 59, 56, 53, 50, …

256 Ϫ19

A swim pass costs $30 for the first month. Each month after that, the
cost is $20 per month. Riley wants to swim for 12 months.

9. The sequence for this situation is arithmetic. What is the 30
first term of this sequence?

10. What is the common difference? 20

11. The 12th term will be the amount Riley spends for a a12 ϭ 30 ϩ11 ͑20 ͒
one year swim pass. Write the equation for finding the
total cost of a one year swim pass.

Copyright © by Holt, Rinehart and Winston. 10 Holt Algebra 1
All rights reserved.