## 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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## Unit 4 - Linear Equations and Linear Systems

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## 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

## This unit does not contain activities.

This is the guided notes, homework assignments, quizzes, study guide, and unit test only. For suggested activities to go with this unit, check out the ATA Activity Alignment Guides .

## This resource is included in the following bundle(s):

Algebra 1 Curriculum Algebra 1 Curriculum (with Activities)

## License Terms:

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## Copyright Terms:

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## 2.4: Graphing Linear Equations- Answers to the Homework Exercises

- Last updated
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- Page ID 45036

- Darlene Diaz
- Santiago Canyon College via ASCCC Open Educational Resources Initiative

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## Graphing and Slope

- \(\frac{1}{3}\)
- \(\frac{4}{3}\)
- \(\frac{1}{2}\)
- \(-\frac{1}{3}\)
- \(\frac{16}{7}\)
- \(-\frac{7}{17}\)
- \(\frac{1}{16}\)
- \(\frac{24}{11}\)
- \(x=\frac{23}{6}\)
- \(y=-\frac{29}{6}\)

## Equations of Lines

- \(y=-\frac{3}{4}x-1\)
- \(y = −6x + 4\)
- \(y = − \frac{1}{4} x + 3\)
- \(y = \frac{1}{3} x + 3\)
- \(y = −3x + 5\)
- \(y = − \frac{1}{10} x − \frac{37}{10}\)
- \(y = \frac{7x}{3} − 8\)
- \(y = −4x + 3\)
- \(y = \frac{1}{10} x − \frac{3}{10}\)
- \(y = − \frac{4}{7} x + 4\)
- \(y=\frac{5}{2}x\)

- \(y − (−5) = 9(x − (−1))\)
- \(y − (−2) = −3(x − 0)\)
- \(y − (−3) = \frac{1}{5} (x − (−5))\)
- \(y − 2 = 0(x − 1)\)
- \(y − (−2) = −2(x − 2)\)
- \(y − 1 = 4(x − (−1))\)
- \(y − (−4) = − \frac{2}{3} (x − (−1))\)
- \(y = − \frac{3}{5} x + 2\)
- \(y = − \frac{3}{2} x + 4\)
- \(y = x − 4\)
- \(y = − \frac{1}{2} x\)
- \(y = − \frac{2}{3} x − \frac{10}{3}\)
- \(y = − \frac{5}{2} x − 5\)
- \(y = −3\)
- \(y − 3 = −2(x + 4)\)
- \(y + 2 = \frac{3}{2} (x + 4)\)
- \(y + 3 = − \frac{8}{7} (x − 3)\)
- \(y − 5 = − \frac{1}{8} (x + 4)\)
- \(y + 4 = −(x + 1)\)
- \(y = − \frac{8}{7} x − \frac{5}{7}\)
- \(y = −x + 2\)
- \(y = − \frac{1}{10} x − \frac{3}{2}\)
- \(y=\frac{1}{3}x+1\)

## Parallel and Perpendicular Lines

- \(m_{||} = 2\)
- \(m_{||} = 1\)
- \(m_{||} = − \frac{2}{3}\)
- \(m_{||} = \frac{6}{5}\)
- \(m_{⊥} = 0\)
- \(m_{⊥} = −3\)
- \(m_{⊥} = 2\)
- \(m_{⊥} = − \frac{1}{3}\)
- \(y − 4 = \frac{9}{2} (x − 3)\)
- \(y − 3 = \frac{7}{5} (x − 2)\)
- \(y + 5 = −(x − 1)\)
- \(y − 2 = \frac{1}{5} (x − 5)\)
- \(y − 2 = − \frac{1}{4} (x − 4)\)
- \(y + 2 = −3(x − 2)\)
- \(y = −2x + 5\)
- \(y = − \frac{4}{3} x − 3\)
- \(y = − \frac{1}{2} x − 3\)
- \(y = − \frac{1}{2} x − 2\)
- \(y = x − 1\)
- \(y=-2x+5\)

## Linear Equations (Algebra 1 Curriculum - Unit 4) | All Things Algebra®

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## Description

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• Linear Equations: Slope Intercept Form vs. Standard Form

• Graphing by Slope Intercept Form

• Writing Linear Equations Given a Graph

• Graphing by Intercepts

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## Unit 4 Linear Equations Homework 2 Answer Key

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Unit 4: Linear Equations Homework 8: Writing Linear Equations REVIEW Direcüons: Write the linear equation in slope-intercept form given the following: 1. slope = Z; ... Unit 4: Linear Equations Homework 10: Parallel & Perpendicular Lines (Day 2) Write an equation passing through the point and PARALLEL to the given line. + 6 5.1 =

Homework Answer Keys Final Exam Materials Calculator TIps Answer keys are listed ... UNIT 5: SOLVING SYSTEMS OF LINEAR EQUATIONS. Homework 1: File Size: 1055 kb: File Type: pdf: Download File. Homework 2: ... Unit 7 Review KEY: File Size: 621 kb: File Type: pdf: Download File. Unit 7 Study Guide KEY:

Linear equations and linear systems: Unit test; Lesson 3: Balanced moves. Learn. Intro to equations with variables on both sides (Opens a modal) Equations with variables on both sides: 20-7x=6x-6 (Opens a modal) Practice. Equations with variables on both sides Get 3 of 4 questions to level up!

Unit 4. 8.4 Linear Equations and Linear Systems. Puzzle Problems. Lesson 1 Number Puzzles; Linear Equations in One Variable. Lesson 2 Keeping the Equation Balanced; Lesson 3 Balanced Moves; Lesson 4 More Balanced Moves; Lesson 5 Solving Any Linear Equation; Lesson 6 Strategic Solving; Lesson 7

Introduction to Systems of Equations and Inequalities; 7.1 Systems of Linear Equations: Two Variables; 7.2 Systems of Linear Equations: Three Variables; 7.3 Systems of Nonlinear Equations and Inequalities: Two Variables; 7.4 Partial Fractions; 7.5 Matrices and Matrix Operations; 7.6 Solving Systems with Gaussian Elimination; 7.7 Solving Systems with Inverses; 7.8 Solving Systems with Cramer's Rule

Unit 1 - Rigid Transformations and Congruence. Unit 2 - Dilations, Similarities, and Introducing Slope. Unit 3 - Linear Relationships. Unit 4 - Linear Equations and Linear Systems. Unit 5 - Functions and Volume. Unit 6 - Associations in Data. Unit 7 - Exponents and Scientific Notation.

Test your understanding of Linear equations, functions, & graphs with these NaN questions. Start test. This topic covers: - Intercepts of linear equations/functions - Slope of linear equations/functions - Slope-intercept, point-slope, & standard forms - Graphing linear equations/functions - Writing linear equations/functions - Interpreting ...

Unit 4: Writing Linear Equations Day Lesson Topic Textbook Section Homework 1 U4: L1 (Notes) Writing Linear Equations in Slope-Intercept Form 5.1 Pg 276-277 # 1-25 ODDS, 28 , 30 2 U4: L1b (Notes) Writing Linear Inequalities Given a Graph in ... (Practice Quiz and Key Online!) n/a "Lab Prep" - 4.1 & 4.2 6 U4: L3 (Notes) Writing Linear ...

Unit 5 - Systems of Linear Equations and Inequalities. This unit begins by ensuring that students understand that solutions to equations are points that make the equation true, while solutions to systems make all equations (or inequalities) true. Graphical and substitution methods for solving systems are reviewed before the development of the ...

Algebra 1 Unit 4:Linear Equations. Algebra 1 Unit 4: Linear Equations. $20.95. Only a nontransferable license is available for this resource. 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. VIEW PREVIEW.

Study with Quizlet and memorize flashcards containing terms like Slope = -8 and y intercept = 5, Slope = 4/3, y intercept = 3, Slope = 0, y intercept = 4 and more. ... Unit 4 Review - Writing Linear Equations. Flashcards; Learn; Test; Match; Q-Chat; Flashcards; Learn; Test; Match; ... RAISE Unit 8 SPN Vocabulary . Teacher 17 terms. k12618 ...

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.

This page titled 1.5: Linear Equations- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

1325. Brielle's piggy bank has all nickels and dimes in it. The total value of the money in her piggy bank is $7.80. If Brielle has 66 nickels, write and solve a linear equation to find the number of dimes she has. 45. Direct, Inverse or Neither: y/3 = x. Direct. Direct, Inverse or Neither: xy = 40. Inverse.

This page titled 2.4: Graphing Linear Equations- Answers to the Homework Exercises is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Darlene Diaz (ASCCC Open Educational Resources Initiative) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

Unit 4 Linear Equations Homework 2 Answer Key. a linear equation is a type of polynomial function which has a degree of 1.i had looked into unit 4 linear equations homework 3 graphing linear equations day 1 answer key many tutoring services, but they weren't affordable and did not understand my custom-written needs.homework 2: file size: 411 kb

Description. This Linear Equations Unit Bundle contains guided notes, homework assignments, three quizzes, study guide and a unit test that cover the following topics: • Slope from a Graph. • Slope from Ordered Pairs (The Slope Formula) • Linear Equations: Slope Intercept Form vs. Standard Form.

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Final answer: The question deals with linear equations and requires understanding of parallel and perpendicular lines in mathematics, focusing on their slopes and y-intercepts in the slope-intercept form y = mx + b. The practice test solution examples provided relate to real-world scenarios represented by linear equations.

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