Unit 5 – Inequalities and Scatterplots 1

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– Unit 5 – [Inequalities and Scatterplots]

Unit 5 – Inequalities and Scatterplots 2

To be a Successful Algebra class,

TIGERs will show…

#TENACITY during our practice, have…

I attempt all practice I attempt all homework I never give up when I don’t understand

#INTEGRITY as we help others with their work, maintain a…

I always check my answers I correct my work, I never just copy answers I explain answers, I never just give them

#GO-FOR-IT attitude, continually…

I write down all notes, even if I’m confused I remain positive about my goals I treat each day as a chance to reset

#ENCOURAGE each other to succeed as a team, and always…

I offer help when I understand the material I push my teammates to reach their goals I never let my teammates give up

#REACH-OUT and ask for help when we need it!

I ask my questions during homework check I ask my teammates for help during practice I attend enrichment/tutorials when I need to

Unit 5 – Inequalities and Scatterplots 3

Unit Calendar

MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY

November 17 18 19 20 21

…

…

…

…

Scatterplots

24 25 26 27 28

Scatterplots

In Class Activity

Student Holiday

Student Holiday

Student Holiday

December 1 2 3 4 5

Graph 1 Variable

Inequalities

Solve 1 Variable

Inequalities

Graph 2 Variable Inequalities

Solve 2 Variable Inequalities

Review

8 9 10 11 12

TEST

Applications of

Inequalities

Review 6-Weeks

TEST

…

Essential Questions

Why is it necessary to write and graph inequalities in real world situations instead of always using equations?

How do I verify a solution to an inequality?

Unit 5 – Inequalities and Scatterplots 4

Critical Vocabulary

Scatterplot

Correlation

Line of Best Fit

Inequality

Less Than

Less Than or Equal to

Greater Than

Greater Than or Equal to

Unit 5 – Inequalities and Scatterplots 5

Scatterplots

Scatterplot: Data from 2 variables are plotted to reveal a possible ____________.

Positive Correlation:

Negative Correlation:

No Correlation:

When there is a correlation, the ______ of ______ ____ is the straight line that BEST models the data. It can be used to make predictions.

Examples:

What’s the correlation?

______The temperature of hot chocolate sitting on a table.

______ The number of pets a person owns and the number of books that person read last year.

______ A person's age and their height in elementary school.

Which of the following equations most

closely represents the line of best fit?

A. y = 2/3x

B. y = x + 4 C. y = 2/3x + 3

D. No correlation

Which of the following equations most

closely represents the line of best fit?

A. y = -x + 6

B. y = -3/4x + 8 C. y = -4/3x + 8

D. No correlation

Practice:

Unit 5 – Inequalities and Scatterplots 6

What’s the correlation?

______ The number of members in a family and the size of the family's grocery bill.

______ The amount of income and the years of education.

______ As temperature get colder, electric bill rises.

______ The more time I spend at the mall, the less money I have.

______ The height of the water in a swimming pool as the pool is drained for cleaning.

______ The length of a person's hair related to their shoe size.

______ The number of hours worked and the paycheck amount.

______ The temperature of a hot oven over a period of time once it is turned off.

Which of the following equations most closely represents the line of best fit?

A. y = 2/3x + 5 B. y = x + 4

C. y = 1/3x + 5 D. No correlation

A. y = x + 2 B. y = 3/4x

C. y = 2/3x + 3 D. No correlation

A. y = x + 2 B. y = 2x + 1

C. y = 1/2x + 5 D. No correlation

A. y = 1/3x + 1 B. y = x

C. y = 2/3x + 1 D. No correlation

A. y = -x + 6

B. y = -4x + 10 C. y = -x + 9

D. No correlation

A. y = -x + 6

B. y = -3/4x + 8 C. y = -4/3x + 8 D. No correlation

Unit 5 – Inequalities and Scatterplots 7

Scatterplots

Examples:

Mr. Thomas wanted to know if the amount

of class time he gave to study before a test affected their test scores. The scatter plot

below shows the results.

What kind of correlation is this?

If they study 13 minutes, what is a good prediction for the average test score?

If the average test score is a 70, what do you predict was the MOST time they spent

studying?

The New York Zoo has been keeping track of the population of a certain type of penguin

over the years.

Year Population

1970 68,000

1980 63,000

1990 59,000

2000 54,000

Based on the data, what is a good prediction for what the population was in 1960?

If the pattern continues, between what years

would we expect the population to drop below 40,000?

A. 2010 – 2020 C. 2030 – 2040

B. 2050 – 2060 D. 2070 – 2080

Unit 5 – Inequalities and Scatterplots 8

Practice:

A piano teacher wanted to see if there was

a correlation between the hours spent practicing and the number of incorrect

notes played. His results are shown below:

What kind of correlation is this?

If they practice 4.5 hours, what is a good prediction for the number of incorrect notes

played?

If there were 8 incorrect notes played, what is a good prediction of the time spent practicing?

Tuan is trying to get faster and faster at

typing, but he notices that the faster he types, the less accurate he is. The

scatterplot below shows some of his data.

What kind of correlation is this?

If Tuan types 65 words per minute, what is a good prediction of his accuracy?

If Tuan types a report with an accuracy of 75%, what is a good prediction of the

speed he was writing?

Continued…

Unit 5 – Inequalities and Scatterplots 9

The table below shows salaries for teachers in a nearby district.

Years of Teaching

Salary

1 $42,000

2 $44,000

3 $45,000

4 $47,000

Based on the data, what is a good prediction for the salary of a teacher with 6 years of experience?

If the pattern continues, about how many years would a teacher need to teach to earn

$60,000?

A. 8 - 10 years C. 16 – 20 years

B. 12 - 15 years D. 22 – 24 years

The New York Zoo has been keeping track of the population of a certain type of penguin

over the years.

Year Population

1970 68,000

1980 63,000

1990 59,000

2000 54,000

If the pattern continues, between what years

would we expect the population to drop below 30,000?

A. 2010 – 2030

B. 2030 – 2050

C. 2050 – 2070

D. 2070 – 2090

Unit 5 – Inequalities and Scatterplots 10

Below is a table of data collected of random students of how much time they watch TV and their test scores.

Graph the data onto the grid. Be sure to label and number your axis.

Time spent watching TV

(hours) Test Score

1 95

1.25 92

4 75

6 60

5.5 70

5 70

3.75 77

2 86

2.5 80

3 75

1.75 78

1. Describe your scatterplot. Where there any patterns that you observed?

2. How does the test scores change with the more time you spend watching TV?

3. Predict the test score of someone who watches 7 hours of TV.

4. Based on this data, if a student wants to score at least an 80, what is the most number of hours they

should spend watching TV?

Unit 5 – Inequalities and Scatterplots 11

Unit 5 – Inequalities and Scatterplots 12

1 Variable Inequalities: Graphing

Symbols used when graphing single variable inequalities:

<

>

≤

≥

Examples: Graph the following Inequality:

m < -5

Graph the following Inequality:

b ≥ 2

Graph the following Inequality:

-2 ≤ x < 6

Write the Inequality for this:

Write the Inequality for this:

Write the Inequality for this:

Practice: Graph the following Inequality:

v ≤ 4

Graph the following Inequality:

x < -3

Graph the following Inequality:

1 < c ≤ 8

Write the Inequality for this:

Write the Inequality for this:

Write the Inequality for this:

Graph the following Inequality: k < 0

Graph the following Inequality: j ≥ -8

Graph the following Inequality: -1 ≤ x < 7

Unit 5 – Inequalities and Scatterplots 13

Examples: Is h=-3 is a solution to the following

inequality? 3h – 4 < -15

Is x=2 is a solution to the following inequality?

6x - 5 ≥ 2x

Solve the following inequality then graph 4y – 8 > 12

Solve the following inequality then graph 16 ≥ 2x + 10

Practice: Is d=4 is a solution to the following inequality?

2d – 5 ≤ -7

Is p=-5 is a solution to the following

inequality? 3p - 5 < 2p

Solve the following inequality then graph

3g + 6 ≤ -9

Solve the following inequality then graph

22 < 5w – 8

Solve the following inequality then graph 10 ≥ 6r – 2

Solve the following inequality then graph 2x + 5 > -3

Unit 5 – Inequalities and Scatterplots 14

1 Variable Inequalities: Solving

<

>

≤

≥

Review Practice:

Find the value of x for which the inequality

3x – 4 > 2x is true.

A. 2

B. 4 C. 5

D. 0

What inequality is represented by this number

line?

A. -8 < x ≤ 4

B. -8 > x ≥ 4 C. -8 ≥ x > 4

D. -8 ≤ x < 4

Which graph represents the solution to the inequality

4x – 6 > -2

A.

B.

C.

D.

Let’s discover a rule about Solving Inequalities…

-12 < 24 Step: Add 3

T / F

-12 < 24 Step: Subtract 4

T / F

-12 < 24 Step: Multiply 2

T / F

-12 < 24 Step: Multiply -2

T / F

-12 < 24 Step: Divide 6

T / F

-12 < 24 Step: Divide -4

T / F

Rule:

Unit 5 – Inequalities and Scatterplots 15

Examples: Solve the following:

2

3x + 9 ≥ -2

Solve the following:

-2x – 6 < -10

Solve the following:

-2x + 8 > -5x + 17

Solve the following:

4x – 5 ≤ 6x + 7

Practice: Solve the following:

4

5x + 3 > 10

Solve the following:

-5x + 3 ≥ -7

Solve the following:

-3x + 8 < -6x + 20

Solve the following:

10x + 5 ≤ 15x + 30

Solve the following: 3

2x – 1 ≥ 4

Solve the following: 9x < 2x + 21

Solve the following: 7x + 2 > 4x + 8

Solve the following: 10x + 2 ≤ 12x + 6

Unit 5 – Inequalities and Scatterplots 16

Unit 5 – Inequalities and Scatterplots 17

2 Variable Inequalities: Graphing

< “Less Than”

> “Greater Than”

≤ “Less Than or Equal to”

≥ “Greater Than or Equal to”

Examples: Graph y > -3x + 1

Graph y ≤ 2/3x – 4

Graph y < -4

Graph x ≥ 5

Practice: Graph y ≥ 2x – 5

Graph y > -1/2x + 6

Graph y ≤ 7

Graph x < -3

Graph y > 2

Graph y < -x + 5

Graph x ≤ 0

Graph y ≥ 2/3x

Unit 5 – Inequalities and Scatterplots 18

Examples: Write the Inequality

for the graph below:

Write the Inequality

for the graph below:

For the graph below,

state if each ordered pair is a solution:

( -1 , 2 ) _______ ( 3 , 0 ) _______ ( -4 , -5 ) _______ ( 0 , 0 ) _______

For the inequality

below, state if each ordered pair is a

solution: 6x – 4y > -5

( -3 , -2 ) _______ ( 3 , 4 ) _______

Practice: Write the Inequality

for the graph below:

Write the Inequality

for the graph below:

For the graph below,

state if each ordered pair is a solution:

( 4 , 0 ) _______ ( -2 , 3 ) _______ ( 0 , 3 ) _______ ( -5 , 6 ) _______

For the inequality

below, state if each ordered pair is a

solution: 4x – 3y ≤ 8

( -3 , 2 ) _______ ( 1 , -2 ) _______ ( 0 , 0 ) _______

Write the Inequality

for the graph below:

Write the Inequality

for the graph below:

Unit 5 – Inequalities and Scatterplots 19

2 Variable Inequalities: Solving

< “Less Than”

> “Greater Than”

≤ “Less Than or Equal to”

≥ “Greater Than or Equal to”

Examples: Graph

3x + y < 4

Graph 3x + 2y ≥ 10

Graph -4x – 5y < 15

Graph -3 ≥ y – 7

Practice: Graph

4x + y ≥ -1

Graph 4x + 3y ≥ 9

Graph 2x – 3y < 18

Graph 3 ≥ x + 1

Unit 5 – Inequalities and Scatterplots 20

Examples: Solve

3(𝑤 + 2) ≥ 21

Solve −3(2𝑑 + 2) < −18

Solve 3(𝑥 − 3) − 5𝑥 ≥ 3

Practice:

Solve 4(𝑝 − 3) < 12

Solve −2(3𝑑 − 1) > 14

Solve 5(𝑥 − 2) − 8𝑥 ≤ 2

Unit 5 – Inequalities and Scatterplots 21

Applications of Inequalities

Examples:

1. For the inequality 0 ≤ x ≤ 50, which of the following choices would a whole number solution, x, be

reasonable?

a. The number of stars in the Milky Way

b. The number of seats in large football stadium

c. The temperature in Alaska in Co, when it is below freezing

d. The number of tickets sold for a play in a theater that has a maximum capacity of 50

2. Sarah wants to buy shirts for her school's graduation party. A company will make the shirts for $10.50

each plus a $50 setup charge. The equation below represents C, the total cost for x number of shirts

purchased.

C = 10.50x + 50

If Sarah has $1000, which inequality could she use to find the maximum number of shirts she can buy?

a. 1000 ≤ 10.50𝑥 + 50

b. 1000 ≥ 10.50𝑥 + 50

c. 1000 < 10.50𝑥 + 50

d. 1000 > 10.50𝑥 + 50

3. Water freezes at 0 degrees and boils at 100 degrees Celsius. Which inequality represents the

temperature between these two points, when the water is neither freezing nor boiling yet.

a. 0 < 𝑥 < 100

b. 0 ≤ 𝑥 ≤ 100

c. 0 > 𝑥 > 100

d. 0 ≥ 𝑥 ≤ 100

4. When you travel on an airplane you are allowed two carry on items whose combined weight cannot

exceed 100 pounds. Which inequality represents the possible weights of your two carry on items?

a. 𝑥 + 𝑦 ≥ 100

b. 𝑥 + 𝑦 ≤ 100

c. 2𝑥 + 2𝑦 ≤ 100

d. 2𝑥 + 2𝑦 ≥ 100

Unit 5 – Inequalities and Scatterplots 22

Practice:

1. Which of the following choices could not be represented by the inequality 20 ≤ x ≤ 38?

a. The temperature on a day when the low was 20o and the high was 38o

b. The total points in a basketball game when Samuel scored 20 points and Barbara scored 38

points

c. The speed Theona is driving when she accelerates from 20 mph to 38 mph

d. The height of a rose bush the month it grew from 20 cm to 38 cm

2. On a road in the city of Katy, the maximum speed is 40 kilometers per hour and the minimum speed is

15 kilometers per hour. If x represents speed, which sentence best expresses this condition?

e. 40 < 𝑥 < 15

f. 40 ≤ 𝑥 ≤ 15

g. 40 > 𝑥 > 15

h. 40 ≥ 𝑥 ≥ 15

3. You are saving up to buy a new video game system for $300. You can earn $8 an hour and have $15

saved up already. Which inequality could be used to solve for the number of hours you need to work

to afford the new system?

a. 15 + 8𝑥 > 300

b. 15 + 8𝑥 < 300

c. 15 + 8𝑥 ≥ 300

d. 15 + 8𝑥 ≤ 300

4. To compete in a piano competition, you need to perform two musical pieces whose combined duration

is no greater than 15 minutes. Which inequality represents the possible duration of your two musical

pieces?

a. 𝑥 + 𝑦 ≥ 15

b. 𝑥 + 𝑦 ≤ 15

c. 2𝑥 + 2𝑦 ≤ 15

d. 2𝑥 + 2𝑦 ≥ 15

5. A carpet cleaner charges a flat fee of $35 plus an additional fee of $12 per room to clean carpets. If

you have $140 dollars, how many rooms can you get cleaned?

a. 35 + 12𝑥 > 140

b. 35 + 12𝑥 < 140

c. 35 + 12𝑥 ≥ 140

d. 35 + 12𝑥 ≤ 140

Unit 5 – Inequalities and Scatterplots 23