writing linear equations from a table practice and problem solving d answer key

ⓐ yes ⓑ yes ⓒ no ⓓ yes ⓔ no

ⓐ no ⓑ yes ⓒ yes ⓓ no ⓔ no

2 · 2 · 2 · 2 · 5 2 · 2 · 2 · 2 · 5

2 · 2 · 3 · 5 2 · 2 · 3 · 5

ⓐ 9 ⓑ 64 ⓒ 40

ⓐ 216 ⓑ 64 ⓒ 185

10 x 2 + 16 x + 17 10 x 2 + 16 x + 17

12 y 2 + 9 y + 7 12 y 2 + 9 y + 7

ⓐ 14 x 2 − 13 14 x 2 − 13 ⓑ 12 x ÷ 2 12 x ÷ 2 ⓒ z + 13 z + 13 ⓓ 8 x − 18 8 x − 18

ⓐ 17 y 2 + 19 17 y 2 + 19 ⓑ 7 y 7 y ⓒ x + 11 x + 11 ⓓ 11 a − 14 11 a − 14

ⓐ 4 ( p + q ) 4 ( p + q ) ⓑ 4 p + q 4 p + q

ⓐ 2 x − 8 2 x − 8 ⓑ 2 ( x − 8 ) 2 ( x − 8 )

w − 7 w − 7

l − 6 l − 6

4 q − 8 4 q − 8

7 n + 3 7 n + 3

ⓐ = = ⓑ > > ⓒ < < ⓓ = =

ⓐ > > ⓑ = = ⓒ > > ⓓ < <

ⓐ −6 −6 ⓑ 2 ⓒ −2 −2

ⓐ −7 −7 ⓑ 3 ⓒ −3 −3

ⓐ 2 ⓑ −2 −2 ⓒ −10 −10 ⓓ 10

ⓐ 3 ⓑ −3 −3 ⓒ −11 −11 ⓓ 11

ⓐ 8 , 8 8 , 8 ⓑ −18 , −18 , −18 −18 ⓒ 19 , 19 19 , 19 ⓓ −4 , −4 , −4 −4

ⓐ 8 , 8 8 , 8 ⓑ −22 , −22 , −22 −22 ⓒ 23 , 23 23 , 23 ⓓ 3 , 3 3 , 3

ⓐ 23 ⓑ 60 ⓒ −63 −63 ⓓ −9 −9

ⓐ 39 ⓑ 39 ⓒ −28 ⓓ −7

ⓐ 81 ⓑ −81 −81

ⓐ 49 ⓑ −49 −49

( 9 + ( −16 ) ) + 4 ; − 3 ( 9 + ( −16 ) ) + 4 ; − 3

( −8 + ( −12 ) ) + 7 ; − 13 ( −8 + ( −12 ) ) + 7 ; − 13

The difference in temperatures was 45 degrees.

The difference in temperatures was 9 degrees.

− 23 40 − 23 40

− 5 8 − 5 8

−33 a −33 a

−26 b −26 b

3 4 b 3 4 b

79 60 79 60

103 60 103 60

ⓐ 27 a − 32 36 27 a − 32 36 ⓑ 2 a 3 2 a 3

ⓐ 24 k − 5 30 24 k − 5 30 ⓑ 2 k 15 2 k 15

− 1 2 − 1 2

ⓐ 6.58 6.58 ⓑ 6.6 6.6 ⓒ 7

ⓐ 15.218 15.218 ⓑ 15.22 15.22 ⓒ 15.2 15.2

ⓐ −16.49 −16.49 ⓑ −0.42 −0.42

ⓐ −23.593 −23.593 ⓑ −12.58 −12.58

−27.4815 −27.4815

−87.6148 −87.6148

ⓐ 25.8 ⓑ 258 ⓒ 2,580

ⓐ 142 ⓑ 1,420 ⓒ 14,200

587.3 587.3

34.25 34.25

ⓐ 117 500 117 500 ⓑ −0.875 −0.875

ⓐ 3 125 3 125 ⓑ −0.375 −0.375

ⓐ 0.09, 0.87, 0.039 ⓑ 17%, 175%, 8.25%

ⓐ 0.03, 0.91, 0.083 ⓑ 41%, 225%, 9.25%

ⓐ 6 ⓑ 13 ⓒ −15 −15

ⓐ 4 ⓑ 14 ⓒ −10 −10

ⓐ 4 , 49 4 , 49 ⓑ −3 , 4 , 49 −3 , 4 , 49 ⓒ −3 , 0. 3 – , 9 5 , 4 , 49 −3 , 0. 3 – , 9 5 , 4 , 49 ⓓ − 2 − 2 ⓔ −3 , − 2 , 0. 3 – , 9 5 , 4 , 49 −3 , − 2 , 0. 3 – , 9 5 , 4 , 49

ⓐ 6 , 121 6 , 121 ⓑ − 25 , −1 , 6 , 121 − 25 , −1 , 6 , 121 ⓒ − 25 , − 3 8 , −1 , 6 , 121 − 25 , − 3 8 , −1 , 6 , 121 ⓓ 2.041975.. . 2.041975.. . ⓔ − 25 , − 3 8 , −1 , 6 , 121 , 2.041975.. . − 25 , − 3 8 , −1 , 6 , 121 , 2.041975.. .

32 r + 29 s 32 r + 29 s

41 m + 6 n 41 m + 6 n

1 7 15 1 7 15

1 2 9 1 2 9

−48 a −48 a

−92 x −92 x

11 25 11 25

ⓐ 0 ⓑ undefined

4 x + 8 4 x + 8

6 x + 42 6 x + 42

5 y + 3 5 y + 3

4 n + 9 4 n + 9

70 + 15 p 70 + 15 p

4 + 35 d 4 + 35 d

−10 + 15 a −10 + 15 a

−56 + 105 y −56 + 105 y

− z + 11 − z + 11

− x + 4 − x + 4

3 − 3 x 3 − 3 x

2 x − 20 2 x − 20

5 x − 66 5 x − 66

7 x − 13 7 x − 13

Section 1.1 Exercises

Divisible by 2, 3, 6

Divisible by 2

Divisible by 3, 5

2 · 43 2 · 43

5 · 7 · 13 5 · 7 · 13

2 · 2 · 2 · 2 · 3 · 3 · 3 2 · 2 · 2 · 2 · 3 · 3 · 3

ⓐ 64 ⓑ 16 ⓒ 7

10 x + 6 10 x + 6

22 a + 1 22 a + 1

17 x 2 + 20 x + 16 17 x 2 + 20 x + 16

ⓐ 5 x 2 − 6 x y 5 x 2 − 6 x y ⓑ 6 y 2 5 x 6 y 2 5 x ⓒ y 2 + 21 y 2 + 21 ⓓ 81 x 2 − 6 x 81 x 2 − 6 x

ⓐ 4 a b 2 + 3 a 2 b 4 a b 2 + 3 a 2 b ⓑ 20 x y 2 20 x y 2 ⓒ m + 15 m + 15 ⓓ 121 x 2 − 9 x 121 x 2 − 9 x

ⓐ 8 ( y − 9 ) 8 ( y − 9 ) ⓑ 8 y − 9 8 y − 9

ⓐ 5 ( 3 x + y ) 5 ( 3 x + y ) ⓑ 15 x + y 15 x + y

2 c + 14 2 c + 14

3 n − 7 3 n − 7

Answers will vary.

Section 1.2 Exercises

ⓐ > > ⓑ > > ⓒ > > ⓓ > >

ⓐ = = ⓑ = = ⓒ > > ⓓ = =

ⓐ −11 −11 ⓑ −3 −3 ⓒ 3 3

ⓐ 6 ⓑ −6 −6 ⓒ −20 −20 ⓓ 20 20

ⓐ −32 −32 ⓑ −65 −65 ⓒ −4 −4 ⓓ 13 13

ⓐ −4 −4 ⓑ −12 −12 ⓒ −39 −39 ⓓ 14 14

ⓐ 64 64 ⓑ −64 −64

ⓐ −47 −47 ⓑ 16 16

( 3 + ( −15 ) ) + 7 ; − 5 ( 3 + ( −15 ) ) + 7 ; − 5

ⓐ 10 − ( −18 ) ; 28 10 − ( −18 ) ; 28 ⓑ −25 − 11 ; − 36 −25 − 11 ; − 36

−6 a + b −6 a + b

− $ 28 − $ 28

Section 1.3 Exercises

− 12 7 − 12 7

10 21 10 21

2 x 2 3 y 2 x 2 3 y

− 21 a 2 11 b 2 − 21 a 2 11 b 2

− 21 50 − 21 50

11 30 11 30

33 4 x 33 4 x

− 4 9 − 4 9

10 u 9 v 10 u 9 v

− 1 16 − 1 16

− 10 9 − 10 9

− 2 5 − 2 5

2 m 3 n 2 m 3 n

29 24 29 24

17 105 17 105

− 53 40 − 53 40

4 x + 3 12 4 x + 3 12

ⓐ 5 6 5 6 ⓑ 4 4

ⓐ 25 n 16 25 n 16 ⓑ 25 n − 16 30 25 n − 16 30

ⓐ −8 x − 15 18 −8 x − 15 18 ⓑ − 10 k 27 − 10 k 27

ⓐ −5 ( a + 1 ) 3 −5 ( a + 1 ) 3 ⓑ a a

49 25 49 25

−28 − 15 y 60 −28 − 15 y 60

33 64 33 64

23 24 23 24

ⓐ 1 5 1 5 ⓑ 6 5 6 5

− 1 9 − 1 9

− 5 11 − 5 11

Section 1.4 Exercises

ⓐ 5.78 ⓑ 5.8 ⓒ 6

ⓐ 0.30 ⓑ 0.3 ⓒ 0

ⓐ 63.48 ⓑ 63.5 ⓒ 63

−40.91 −40.91

−7.22 −7.22

−27.5 −27.5

102.212 102.212

51.31 51.31

−4.89 −4.89

−1200.47982 −1200.47982

337.8914 337.8914

1.305 1.305

$ 2.44 $ 2.44

19 200 19 200

−12.4 −12.4

0.393 0.393

156 % 156 %

6.25 % 6.25 %

ⓐ 0 , 36 , 9 0 , 36 , 9 ⓑ −8 , 0 , 36 , 9 −8 , 0 , 36 , 9 ⓒ −8 , 0 , 12 5 , 36 , 9 −8 , 0 , 12 5 , 36 , 9 ⓓ 1.95286... , 1.95286... , ⓔ −8 , 0 , 1.95286... , 12 5 , 36 , 9 −8 , 0 , 1.95286... , 12 5 , 36 , 9

ⓐ none ⓑ − 100 , −7 , −1 − 100 , −7 , −1 ⓒ − 100 , −7 , − 8 3 , −1 , 0.77 , 3 1 4 − 100 , −7 , − 8 3 , −1 , 0.77 , 3 1 4 ⓓ none ⓔ − 100 , −7 , − 8 3 , −1 , 0.77 , 3 1 4 − 100 , −7 , − 8 3 , −1 , 0.77 , 3 1 4

Section 1.5 Exercises

27 m + ( −21 n ) 27 m + ( −21 n )

5 4 g + 1 2 h 5 4 g + 1 2 h

2.43 p + 8.26 q 2.43 p + 8.26 q

1 5 6 1 5 6

14.88 14.88

49 11 49 11

32 y + 72 32 y + 72

6 c − 78 6 c − 78

3 4 q + 3 3 4 q + 3

5 y − 3 5 y − 3

3 + 8 r 3 + 8 r

36 d + 90 36 d + 90

r s − 18 r r s − 18 r

y p + 4 p y p + 4 p

−28 p − 7 −28 p − 7

−3 x + 18 −3 x + 18

−3 x + 7 −3 x + 7

−3 y − 8 −3 y − 8

−33 c + 26 −33 c + 26

− a + 19 − a + 19

4 m − 10 4 m − 10

72 x − 25 72 x − 25

22 n + 9 22 n + 9

6 c + 34 6 c + 34

12 y + 63 12 y + 63

Review Exercises

Divisible by 2 , 3 , 5 , 6 , 10 2 , 3 , 5 , 6 , 10

6 x 2 − x + 5 6 x 2 − x + 5

ⓐ 11 ( y − 2 ) 11 ( y − 2 ) ⓑ 11 y − 2 11 y − 2

ⓐ 8 ⓑ −8 −8 ⓒ −22 −22 ⓓ 22

ⓐ −3 −3 ⓑ −15 −15 ⓒ −56 −56 ⓓ 17

( −4 + ( −9 ) ) + 23 ; 10 ( −4 + ( −9 ) ) + 23 ; 10

− 15 x 3 11 y 2 − 15 x 3 11 y 2

8 x 15 y 8 x 15 y

31 36 31 36

ⓐ 11 8 11 8 ⓑ 5 6 5 6

− 1 6 − 1 6

− 1 5 − 1 5

96.978 96.978

− 48 5 − 48 5

1. 27 ¯ 1. 27 ¯

4.75 % 4.75 %

no real number

3 4 x + y 3 4 x + y

1 11 15 1 11 15

8 b + 10 8 b + 10

x p − 5 p x p − 5 p

−6 x − 6 −6 x − 6

6 y + 16 6 y + 16

Practice Test

7 n + 7 7 n + 7

−8 − 11 ; − 19 −8 − 11 ; − 19

( −8 − ( −3 ) ) + 5 ; 0 ( −8 − ( −3 ) ) + 5 ; 0

ⓐ 28.15 28.15 ⓑ 28.146 28.146

15 17 15 17

− 5 3 − 5 3

− 7 6 − 7 6

−65.4 −65.4

1 8 13 1 8 13

13 y − 3 13 y − 3

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• Book title: Intermediate Algebra 2e
• Publication date: May 6, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
• Section URL: https://openstax.org/books/intermediate-algebra-2e/pages/chapter-1

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How to Write Linear Equations? (+FREE Worksheet!)

In this article, you learn how to write the equation of the lines by using their slope and one point or using two points on the line.

Related Topics

• How to Find Midpoint
• How to Find Slope
• How to Graph Linear Inequalities
• How to Find Distance of Two Points
• How to Graph Lines by Using Standard Form

Step by step guide to writing linear equations

• The equation of a line in slope intercept form is: \(\color{blue}{y=mx+b}\)
• Identify the slope.
• Find the \(y\)–intercept. This can be done by substituting the slope and the coordinates of a point \((x, y)\) on the line.

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The Ultimate Algebra Bundle From Pre-Algebra to Algebra II

Writing linear equations – example 1:.

What is the equation of the line that passes through \((1, -2)\) and has a slope of \(6\)?

The general slope-intercept form of the equation of a line is \(y=mx+b\), where \(m\) is the slope and \(b\) is the \(y\)-intercept. By substitution of the given point and given slope, we have: \(-2=(6)(1)+b → -2=6+b \) So, \(b= -2-6=-8\), and the required equation is \(y=6x-8\).

Writing Linear Equations – Example 2:

Write the equation of the line through \((1, 1)\) and \((-1, 3)\).

Slop \(= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{3- 1}{-1- 1}=\frac{2}{-2}=-1 → m=-1\) To find the value of \(b\), you can use either point. The answer will be the same: \(y=-x+b \) \((1,1) →1=-1+b→ 1+1=b → b=2\) \((-1,3)→3=-(-1)+b→3-1=b → b=2\) The equation of the line is: \(y=-x+2\)

Writing Linear Equations – Example 3:

What is the equation of the line that passes through \((2,–2)\) and has a slope of \(7\)?

The general slope-intercept form of the equation of a line is \(y=mx+b\), where \(m\) is the slope and \(b\) is the \(y-\)intercept. By substitution of the given point and given slope, we have: \(-2=(7)(2)+b → -2=14+b \) So, \(b= –2-14=-16\), and the required equation is \(y=7x-16\).

The Best Book to Help You Ace Pre-Algebra

Pre-Algebra for Beginners The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Writing linear equations – example 4:.

Write the equation of the line through \((2,1)\) and \((-1,4)\).

Slop \(= \frac{y_{2}- y_{1}}{x_{2} – x_{1} }=\frac{4- 1}{-1- 2}=\frac{3}{-3}=-1 → m= -1\) You can use either point to find the value of \(b\). The answer will be the same: \(y= -x+b \) \( (2,1) →1=-2+b→1+2=b → b=3\) \( (-1,4)→4=-(-1)+b→4-1=b → b=3\) The equation of the line is: \(y=-x+3\)

Exercises for Writing Linear Equations

Write the slope–intercept form of the equation of the line through the given points..

• \(\color{blue}{through: (– 4, – 2), (– 3, 5)}\)
• \(\color{blue}{through: (5, 4), (– 4, 3) }\)
• \(\color{blue}{through: (0, – 2), (– 5, 3) }\)
• \(\color{blue}{through: (– 1, 1), (– 2, 6) }\)
• \(\color{blue}{through: (0, 3), (– 4, – 1) }\)
• \(\color{blue}{through: (0, 2), (1, – 3) }\)

Download Writing Linear Equations Worksheet

• \(\color{blue}{y = 7x + 26}\)
• \(\color{blue}{y = \frac{1}{9} x + \frac{31}{9}}\)
• \(\color{blue}{y =\space – x – 2}\)
• \(\color{blue}{y =\space –5x – 4}\)
• \(\color{blue}{y = x + 3}\)
• \(\color{blue}{y =\space – 5x + 2}\)

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Pre-algebra in 10 days the most effective pre-algebra crash course, college algebra practice workbook the most comprehensive review of college algebra, high school algebra i a comprehensive review and step-by-step guide to mastering high school algebra 1, 10 full length clep college algebra practice tests the practice you need to ace the clep college algebra test.

by: Effortless Math Team about 4 years ago (category: Articles , Free Math Worksheets )

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Pre-Algebra Practice Workbook The Most Comprehensive Review of Pre-Algebra

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Unit 4: Linear equations & graphs

About this unit.

Let's explore different ways to find and visualize slopes and intercepts, and how these concepts can help us solve real-world problems.

Two-variable linear equations intro

• Two-variable linear equations intro (Opens a modal)
• Solutions to 2-variable equations (Opens a modal)
• Worked example: solutions to 2-variable equations (Opens a modal)
• Completing solutions to 2-variable equations (Opens a modal)
• Solutions to 2-variable equations Get 3 of 4 questions to level up!
• Complete solutions to 2-variable equations Get 3 of 4 questions to level up!
• Intro to slope (Opens a modal)
• Positive & negative slope (Opens a modal)
• Worked example: slope from graph (Opens a modal)
• Graphing a line given point and slope (Opens a modal)
• Calculating slope from tables (Opens a modal)
• Worked example: slope from two points (Opens a modal)
• Slope review (Opens a modal)
• Slope from graph Get 3 of 4 questions to level up!
• Graphing from slope Get 3 of 4 questions to level up!
• Slope in a table Get 3 of 4 questions to level up!
• Slope from two points Get 3 of 4 questions to level up!

Horizontal & vertical lines

• Slope of a horizontal line (Opens a modal)
• Horizontal & vertical lines (Opens a modal)
• Horizontal & vertical lines Get 5 of 7 questions to level up!

x-intercepts and y-intercepts

• Intro to intercepts (Opens a modal)
• x-intercept of a line (Opens a modal)
• Intercepts from an equation (Opens a modal)
• Intercepts from a table (Opens a modal)
• Intercepts of lines review (x-intercepts and y-intercepts) (Opens a modal)
• Intercepts from a graph Get 3 of 4 questions to level up!
• Intercepts from an equation Get 3 of 4 questions to level up!
• Intercepts from a table Get 3 of 4 questions to level up!

Applying intercepts and slope

• Slope, x-intercept, y-intercept meaning in context (Opens a modal)
• Slope and intercept meaning in context (Opens a modal)
• Slope and intercept meaning from a table (Opens a modal)
• Finding slope and intercepts from tables (Opens a modal)
• Linear functions word problem: fuel (Opens a modal)
• Relating linear contexts to graph features Get 5 of 7 questions to level up!
• Using slope and intercepts in context Get 3 of 4 questions to level up!
• Linear equations word problems: tables Get 3 of 4 questions to level up!
• Linear equations word problems: graphs Get 3 of 4 questions to level up!
• Graphing linear relationships word problems Get 3 of 4 questions to level up!

Modeling with linear equations and inequalities

• Comparing linear rates example (Opens a modal)
• Linear equations & graphs: FAQ (Opens a modal)
• Creativity break: How do you apply creativity in algebra (Opens a modal)
• Comparing linear rates word problems Get 3 of 4 questions to level up!

Writing Linear Equations from Tables Notes & Practice

• Easel Activity

What educators are saying

Description.

Writing Equations of the form y = mx + b from tables.

This is a one-sided notes page on how to write linear equations from tables. There are nine examples. In some of the examples, the y-intercept is missing, so the student needs to extend the pattern in the table to find it. In other examples, points are missing and so there seems to be no pattern. Students can either write a new table to find the missing values to verify that the table does represent a linear situation (this would be the preferred method) or can find the slope between two points from the table.

Two examples "don't work" as one is not a function and the other is not linear and in the final example, the points are out of order and some are missing.

Also included is an independent practice page with 9 more questions that can be assigned for homework. Key included.

Also available: Writing Equations of Lines from Tables Digital Drag & Drop Activity

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