unit 4 linear equations answer key homework 5

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Unit 4: Linear equations and linear systems

Lesson 3: balanced moves.

• Intro to equations with variables on both sides (Opens a modal)
• Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
• Equations with variables on both sides Get 3 of 4 questions to level up!

Lesson 4: More balanced moves

• Equations with parentheses (Opens a modal)
• Equations with parentheses Get 3 of 4 questions to level up!

Lesson 5: Solving any linear equation

• Multi-step equations review (Opens a modal)

Lesson 6: Strategic solving

• No videos or articles available in this lesson
• Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!
• Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!

Extra practice: Linear equations

• Sums of consecutive integers (Opens a modal)
• Sum of integers challenge (Opens a modal)
• Equation practice with vertical angles (Opens a modal)
• Equation practice with complementary angles (Opens a modal)
• Equation practice with supplementary angles (Opens a modal)
• Sums of consecutive integers Get 3 of 4 questions to level up!
• Equation practice with vertical angles Get 3 of 4 questions to level up!
• Equation practice with angle addition Get 3 of 4 questions to level up!

Lesson 7: All, some, or no solutions

• Creating an equation with no solutions (Opens a modal)
• Creating an equation with infinitely many solutions (Opens a modal)
• Number of solutions to equations challenge Get 3 of 4 questions to level up!

Lesson 8: How many solutions?

• Number of solutions to equations (Opens a modal)
• Worked example: number of solutions to equations (Opens a modal)
• Number of solutions to equations Get 3 of 4 questions to level up!

Lesson 9: When are they the same?

• Age word problem: Imran (Opens a modal)
• Age word problem: Ben & William (Opens a modal)
• Age word problem: Arman & Diya (Opens a modal)
• Age word problems Get 3 of 4 questions to level up!

Lesson 10: On or off the line?

• Solutions of systems of equations Get 3 of 4 questions to level up!

Lesson 12: Systems of equations

• Systems of equations: trolls, tolls (1 of 2) (Opens a modal)
• Systems of equations: trolls, tolls (2 of 2) (Opens a modal)
• Systems of equations with graphing (Opens a modal)
• Systems of equations with graphing: y=7/5x-5 & y=3/5x-1 (Opens a modal)
• Systems of equations with graphing Get 3 of 4 questions to level up!
• Number of solutions to a system of equations graphically Get 3 of 4 questions to level up!

Lesson 13: Solving systems of equations

• Systems of equations with substitution: y=-1/4x+100 & y=-1/4x+120 (Opens a modal)
• Number of solutions to a system of equations graphically (Opens a modal)
• Number of solutions to system of equations review (Opens a modal)
• Number of solutions to a system of equations algebraically Get 3 of 4 questions to level up!

Lesson 14: Solving more systems

• Systems of equations with substitution: 2y=x+7 & x=y-4 (Opens a modal)
• Systems of equations with substitution (Opens a modal)
• Systems of equations with substitution: y=4x-17.5 & y+2x=6.5 (Opens a modal)
• Systems of equations with substitution: y=-5x+8 & 10x+2y=-2 (Opens a modal)
• Substitution method review (systems of equations) (Opens a modal)
• Systems of equations with substitution Get 3 of 4 questions to level up!

Lesson 16: Solving problems with systems of equations

• System of equations word problem: no solution (Opens a modal)
• Systems of equations with substitution: coins (Opens a modal)
• Systems of equations word problems Get 3 of 4 questions to level up!

4.1 Linear Functions

m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; m = 4 − 3 0 − 2 = 1 − 2 = − 1 2 ; decreasing because m < 0. m < 0.

y = − 7 x + 3 y = − 7 x + 3

H ( x ) = 0.5 x + 12.5 H ( x ) = 0.5 x + 12.5

Possible answers include ( − 3 , 7 ) , ( − 3 , 7 ) , ( − 6 , 9 ) , ( − 6 , 9 ) , or ( − 9 , 11 ) . ( − 9 , 11 ) .

( 16 , 0 ) ( 16 , 0 )

• ⓐ f ( x ) = 2 x ; f ( x ) = 2 x ;
• ⓑ g ( x ) = − 1 2 x g ( x ) = − 1 2 x

y = – 1 3 x + 6 y = – 1 3 x + 6

4.2 Modeling with Linear Functions

ⓐ C ( x ) = 0.25 x + 25 , 000 C ( x ) = 0.25 x + 25 , 000 ⓑ The y -intercept is ( 0 , 25 , 000 ) ( 0 , 25 , 000 ) . If the company does not produce a single doughnut, they still incur a cost of $25,000.

ⓐ 41,100 ⓑ 2020

21.57 miles

4.3 Fitting Linear Models to Data

54 ° F 54 ° F

150.871 billion gallons; extrapolation

4.1 Section Exercises

Terry starts at an elevation of 3000 feet and descends 70 feet per second.

d ( t ) = 100 − 10 t d ( t ) = 100 − 10 t

The point of intersection is ( a , a ) . ( a , a ) . This is because for the horizontal line, all of the y y coordinates are a a and for the vertical line, all of the x x coordinates are a . a . The point of intersection is on both lines and therefore will have these two characteristics.

y = 3 5 x − 1 y = 3 5 x − 1

y = 3 x − 2 y = 3 x − 2

y = − 1 3 x + 11 3 y = − 1 3 x + 11 3

y = − 1.5 x − 3 y = − 1.5 x − 3

perpendicular

f ( 0 ) = − ( 0 ) + 2 f ( 0 ) = 2 y − int : ( 0 , 2 ) 0 = − x + 2 x − int : ( 2 , 0 ) f ( 0 ) = − ( 0 ) + 2 f ( 0 ) = 2 y − int : ( 0 , 2 ) 0 = − x + 2 x − int : ( 2 , 0 )

h ( 0 ) = 3 ( 0 ) − 5 h ( 0 ) = − 5 y − int : ( 0 , − 5 ) 0 = 3 x − 5 x − int : ( 5 3 , 0 ) h ( 0 ) = 3 ( 0 ) − 5 h ( 0 ) = − 5 y − int : ( 0 , − 5 ) 0 = 3 x − 5 x − int : ( 5 3 , 0 )

− 2 x + 5 y = 20 − 2 ( 0 ) + 5 y = 20 5 y = 20 y = 4 y − int : ( 0 , 4 ) − 2 x + 5 ( 0 ) = 20 x = − 10 x − int : ( − 10 , 0 ) − 2 x + 5 y = 20 − 2 ( 0 ) + 5 y = 20 5 y = 20 y = 4 y − int : ( 0 , 4 ) − 2 x + 5 ( 0 ) = 20 x = − 10 x − int : ( − 10 , 0 )

Line 1: m = –10 Line 2: m = –10 Parallel

Line 1: m = –2 Line 2: m = 1 Neither

Line 1 :   m = – 2       Line 2 :   m = – 2       Parallel Line 1 :   m = – 2       Line 2 :   m = – 2       Parallel

y = 3 x − 3 y = 3 x − 3

y = − 1 3 t + 2 y = − 1 3 t + 2

y = − 5 4 x + 5 y = − 5 4 x + 5

y = 3 x − 1 y = 3 x − 1

y = − 2.5 y = − 2.5

y = 3 y = 3

x = − 3 x = − 3

Linear, g ( x ) = − 3 x + 5 g ( x ) = − 3 x + 5

Linear, f ( x ) = 5 x − 5 f ( x ) = 5 x − 5

Linear, g ( x ) = − 25 2 x + 6 g ( x ) = − 25 2 x + 6

Linear, f ( x ) = 10 x − 24 f ( x ) = 10 x − 24

f ( x ) = − 58 x + 17.3 f ( x ) = − 58 x + 17.3

• ⓐ a = 11,900 , b = 1000.1 a = 11,900 , b = 1000.1
• ⓑ q ( p ) = 1000 p – 100 q ( p ) = 1000 p – 100

y = − 16 3 y = − 16 3

x = a x = a

y = d c – a x – a d c – a y = d c – a x – a d c – a

y = 100 x – 98 y = 100 x – 98

x < 1999 201 , x > 1999 201 x < 1999 201 , x > 1999 201

$45 per training session.

The rate of change is 0.1. For every additional minute talked, the monthly charge increases by $0.1 or 10 cents. The initial value is 24. When there are no minutes talked, initially the charge is $24.

The slope is –400. this means for every year between 1960 and 1989, the population dropped by 400 per year in the city.

4.2 Section Exercises

Determine the independent variable. This is the variable upon which the output depends.

To determine the initial value, find the output when the input is equal to zero.

6 square units

20.01 square units

P ( t ) = 75 , 000 + 2500 t P ( t ) = 75 , 000 + 2500 t

(–30, 0) Thirty years before the start of this model, the town had no citizens. (0, 75,000) Initially, the town had a population of 75,000.

Ten years after the model began

W ( t ) = 0.5 t + 7.5 W ( t ) = 0.5 t + 7.5

( − 15 , 0 ) ( − 15 , 0 ) : The x -intercept is not a plausible set of data for this model because it means the baby weighed 0 pounds 15 months prior to birth. ( 0 , 7 . 5 ) ( 0 , 7 . 5 ) : The baby weighed 7.5 pounds at birth.

At age 5.8 months

C ( t ) = 12 , 025 − 205 t C ( t ) = 12 , 025 − 205 t

( 58 . 7 , 0 ) : ( 58 . 7 , 0 ) : In roughly 59 years, the number of people inflicted with the common cold would be 0. ( 0 , 12 , 0 25 ) ( 0 , 12 , 0 25 ) Initially there were 12,025 people afflicted by the common cold.

y = − 2 t +180 y = − 2 t +180

In 2070, the company’s profit will be zero.

y = 3 0 t − 3 00 y = 3 0 t − 3 00

(10, 0) In the year 1990, the company’s profits were zero

During the year 1933

• ⓐ 696 people
• ⓒ 174 people per year
• ⓓ 305 people
• ⓔ P(t) = 305 + 174t
• ⓕ 2,219 people
• ⓐ C(x) = 0.15x + 10
• ⓑ The flat monthly fee is $10 and there is a $0.15 fee for each additional minute used

P(t) = 190t + 4,360

• ⓐ R ( t ) = − 2 . 1 t   +   16 R ( t ) = − 2 . 1 t   +   16
• ⓑ 5.5 billion cubic feet
• ⓒ During the year 2017

More than 133 minutes

More than $42,857.14 worth of jewelry

More than $66,666.67 in sales

4.3 Section Exercises

When our model no longer applies, after some value in the domain, the model itself doesn’t hold.

We predict a value outside the domain and range of the data.

The closer the number is to 1, the less scattered the data, the closer the number is to 0, the more scattered the data.

61.966 years

Interpolation. About 60 ° F . 60 ° F .

This value of r indicates a strong negative correlation or slope, so C This value of r indicates a strong negative correlation or slope, so C

This value of r indicates a weak negative correlation, so B This value of r indicates a weak negative correlation, so B

Yes, trend appears linear because r = 0. 985 r = 0. 985 and will exceed 12,000 near midyear, 2016, 24.6 years since 1992.

y = 1 . 64 0 x + 13 . 8 00 , y = 1 . 64 0 x + 13 . 8 00 , r = 0. 987 r = 0. 987

y = − 0.962 x + 26.86 ,       r = − 0.965 y = − 0.962 x + 26.86 ,       r = − 0.965

y = − 1 . 981 x + 6 0. 197; y = − 1 . 981 x + 6 0. 197; r = − 0. 998 r = − 0. 998

y = 0. 121 x − 38.841 , r = 0.998 y = 0. 121 x − 38.841 , r = 0.998

( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; ( −2 , −6 ) , ( 1 , −12 ) , ( 5 , −20 ) , ( 6 , −22 ) , ( 9 , −28 ) ; Yes, the function is a good fit.

( 189 .8 , 0 ) ( 189 .8 , 0 ) If 18,980 units are sold, the company will have a profit of zero dollars.

y = 0.00587 x + 1985 .4 1 y = 0.00587 x + 1985 .4 1

y = 2 0. 25 x − 671 . 5 y = 2 0. 25 x − 671 . 5

y = − 1 0. 75 x + 742 . 5 0 y = − 1 0. 75 x + 742 . 5 0

Review Exercises

y = − 3 x + 26 y = − 3 x + 26

y = 2 x − 2 y = 2 x − 2

Not linear.

( –9 , 0 ) ; ( 0 , –7 ) ( –9 , 0 ) ; ( 0 , –7 )

Line 1: m = − 2 ; m = − 2 ; Line 2: m = − 2 ; m = − 2 ; Parallel

y = − 0.2 x + 21 y = − 0.2 x + 21

More than 250

y = − 3 00 x + 11 , 5 00 y = − 3 00 x + 11 , 5 00

• ⓑ 100 students per year
• ⓒ P ( t ) = 1 00 t + 17 00 P ( t ) = 1 00 t + 17 00

Extrapolation

y = − 1.294 x + 49.412 ;   r = − 0.974 y = − 1.294 x + 49.412 ;   r = − 0.974

Practice Test

y = −1.5x − 6

y = −2x − 1

Perpendicular

(−7, 0); (0, −2)

y = −0.25x + 12

Slope = −1 and y-intercept = 6

y = 875x + 10,625

• ⓑ dropped an average of 46.875, or about 47 people per year
• ⓒ y = −46.875t + 1250

In early 2018

y = 0.00455x + 1979.5

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All Things Algebra®

Algebra 1 Unit 4: Linear Equations

This unit includes 73 pages of guided notes, homework assignments, three quizzes, a study guide, and a unit test that cover the topics listed in the description below.

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This unit contains the following topics:

• Slope from a Graph • Slope from Ordered Pairs (The Slope Formula) • Linear Equations: Slope Intercept Form vs. Standard Form • Graphing by Slope Intercept Form • Writing Linear Equations Given a Graph • Graphing by Intercepts • Vertical vs. Horizontal Lines • Writing Linear Equations given Point and Slope • Writing Linear Equations given Two Points • Linear Equation Word Problems • Parallel vs. Perpendicular Lines • Scatter Plots & Line of Best Fit • Linear Regression

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Unit 4 – Linear Functions and Arithmetic Sequences

This unit is all about understanding linear functions and using them to model real world scenarios.  Fluency in interpreting the parameters of linear functions is emphasized as well as setting up linear functions to model a variety of situations. Linear inequalities are also taught. The unit ends with a introduction to sequences with an emphasis on arithmetic.

Proportional Relationships

LESSON/HOMEWORK

LECCIÓN/TAREA

LESSON VIDEO

EDITABLE LESSON

EDITABLE KEY

Unit Conversions

Nonproportional Linear Relationships

More Work Graphing Linear Functions

Writing Equations in Slope-Intercept Form

Modeling with Linear Functions

More Linear Modeling

Strange Lines – Vertical and Horizontal

Absolute Value and Step Functions

The Truth About Graphs

Graphs of Linear Inequalities

Introduction to Sequences

Arithmetic Sequences

Unit Review

Unit #4 Review – Linear Functions and Arithmetic Sequences

UNIT REVIEW

REPASO DE LA UNIDAD

EDITABLE REVIEW

Unit #4 Assessment Form A

EDITABLE ASSESSMENT

Unit #4 Assessment Form B

Unit #4 Assessment Form C

Unit #4 Assessment Form D

Unit #4 Exit Tickets

Unit #4 Mid-Unit Quiz (Through Lesson #7) – Form A

Unit #4 Mid-Unit Quiz (Through Lesson #7) – Form B

Unit #4 Mid-Unit Quiz (Through Lesson #7) – Form C

U04.AO.01 – Writing the Equation of a Line Given Two Points.Extra Practice (After Lesson #6)

EDITABLE RESOURCE

U04.AO.02 Performance Task – Linear Modeling (After Lesson #7)

U04.AO.03 – Lesson #9.5 – Absolute Value Equations

U04.AO.04 – Turning Patterns into Sequences (after Lesson #13) – Enrichment Lesson

U04.AO.05 – Linear Modeling of Population (Extended Problem)

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