lesson 6 homework practice write linear equations answer key

Lesson 6 Homework Practice Write Linear Equations Answer Key

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How to Write Linear Equations in Point-Slope and Slope-Intercept Forms

In this article, we will learn how to write linear equations in two different forms: point-slope form and slope-intercept form. These forms are useful for graphing lines, finding their slopes and intercepts, and solving systems of linear equations.

A linear equation is an equation that can be written in the form ax + by = c, where a, b, and c are constants and x and y are variables. A linear equation represents a straight line on a coordinate plane.

Point-Slope Form

The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope of the line and (x1, y1) is any point on the line. To write a linear equation in point-slope form, we need to know the slope of the line and one point on the line.

For example, suppose we want to write a linear equation that passes through the point (-5, 6) and has a slope of 3. We can plug these values into the point-slope form:

y - 6 = 3(x - (-5))

We can simplify this equation by distributing the 3 and adding 6 to both sides:

y = 3x + 21

Slope-Intercept Form

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept of the line. The y-intercept is the point where the line crosses the y-axis, or the value of y when x = 0. To write a linear equation in slope-intercept form, we need to know the slope of the line and the y-intercept of the line.

For example, suppose we want to write a linear equation that passes through the point (0, 1) and has a slope of 2. We can plug these values into the slope-intercept form:

To find the value of b, we can substitute x = 0 and y = 1:

1 = 2(0) + bb = 1

Therefore, the equation in slope-intercept form is:

In lesson 6 homework practice, you will practice writing linear equations in point-slope form and slope-intercept form for different lines. You can check your answers using this answer key[^1^]. Remember to show your work and explain your reasoning.

#Slope-Intercept FormPoint-Slope Form

1.y = 3x + 21y - 6 = 3(x - (-5))

2.y = -4x + 9y - 9 = -4(x - (-5))

3.y = 2x + 1y - 1 66dfd1ed39

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Glencoe McGraw-Hill Algebra 1, Grade: 9 Publisher: Glencoe/McGraw-Hill

Glencoe mcgraw-hill algebra 1, title : glencoe mcgraw-hill algebra 1, publisher : glencoe/mcgraw-hill, isbn : 0078738229, isbn-13 : 9780078738227, use the table below to find videos, mobile apps, worksheets and lessons that supplement glencoe mcgraw-hill algebra 1., textbook resources.

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Be Prepared

18 x + 30 18 x + 30

3 − 2 n 3 − 2 n

2 x − 6 2 x − 6

0.045 0.045

w − 3 w − 3

0.35 x + 0.4 0.35 x + 0.4

2 c + 3 2 c + 3

0.042 0.042

15 15 is greater than x x .

15 < x 15 < x

2 5 x + 4 2 5 x + 4

− x + 4 − x + 4

a. >; b. >; c. >; d. >

m = 2 m = 2

a = 0 a = 0

u = 2 u = 2

x = 4 x = 4

p = −2 p = −2

q = −8 q = −8

y = − 17 5 y = − 17 5

z = 0 z = 0

identity; all real numbers

conditional equation; q = − 9 11 q = − 9 11

conditional equation; k = 201 14 k = 201 14

contradiction; no solution

x = 1 2 x = 1 2

x = −2 x = −2

x = 12 x = 12

u = −12 u = −12

n = 2 n = 2

m = −1 m = −1

r = 1 r = 1

s = −8 s = −8

n = 9 n = 9

d = 16 d = 16

He bought two notebooks.

He did seven crosswords puzzles.

−15 , −8 −15 , −8

−29 , 11 −29 , 11

−33 , −32 , −31 −33 , −32 , −31

−13 , −12 , −11 −13 , −12 , −11

−10 , −8 , −6 −10 , −8 , −6

The average cost was $5,000.

The median price was $19,300.

ⓐ 36 ⓑ $26 ⓒ 125 % 125 %

ⓐ 33 ⓑ $36 ⓐ 175 % 175 %

8.8 % 8.8 %

ⓐ $600 ⓑ $1,800

ⓐ $2,975 ⓑ $11,475

He will earn $2,500.

She earned $7,020.

The rate of simple interest was 6%.

The rate of simple interest was 5.5%.

He paid $17,590.

She deposited $9,600.

b = 2 A h b = 2 A h

h = 2 A b h = 2 A b

C = 5 9 ( F − 32 ) C = 5 9 ( F − 32 )

b = 2 A − B h h b = 2 A − B h h

t = A − P P r t = A − P P r

r = A − P P t r = A − P P t

y = 9 − 4 x 7 y = 9 − 4 x 7

y = 1 − 5 x 8 y = 1 − 5 x 8

The window’s height is 12 meters.

The length of the base is 6 feet.

The measures of the angles are 20°, 70°, and 90°.

The measures of the angles are 30°, 60°, and 90°.

The length of the leg is 8.

The length of the leg is 12.

The length is 39 inches and the width is 16 inches.

The length is 17 yards and the width is 26 yards.

The lengths of the sides of the triangle are 5, 11 and 12 inches.

The lengths of the sides of the triangle are 4, 7 and 9 feet.

The length of the swimming pool is 70 feet and the width is 30 feet.

The length of the garden is 90 yards and the width is 60 yards.

The ladder reaches 12 feet.

He should attach the lights 8 feet from the base of the mast.

Jess has 41 nickels and 18 quarters.

Elane has 22 nickels and 59 dimes.

Eric bought thirty-two 49-cent stamps and twelve 35-cent stamps.

Kailee bought twenty-six 49-cent stamps and ten 20-cent stamps.

84 adult tickets, 31 student tickets

615 children’s tickets and 195 adult tickets

Orlando mixed five pounds of cereal squares and 25 pounds of nuts.

Becca mixed 21 gallons of fruit punch and seven gallons of soda.

The speed of the local train is 48 mph and the speed of the express train is 60 mph.

Jeromy drove at a speed of 80 mph and his mother drove 60 mph.

Christopher’s speed was 50 mph and his parents’ speed was 40 mph.

Ashley’s parents drove 55 mph and Ashley drove 62 mph.

Pierre and Monique will be 429 miles apart in 3 hours.

Thanh and Nhat will be 330 miles apart in 2.2 hours.

Suzy’s speed uphill is 1.8 1.8 mph and downhill is three mph.

The boat’s speed upstream is eight mph and downstream is12 mph.

Hamilton drove 40 mph in the city and 70 mph in the desert.

Phuong rode uphill at a speed of 12 mph and on the flat street at 20 mph.

Angie can buy 7 packs of juice.

Daniel can have 11 people at the party.

Sergio and Lizeth can travel no more than 500 miles.

Rameen can use no more than 76 therms.

Caleb must work at least 96 hours.

Elliot must work at least 85 jobs.

Brenda must babysit at least 27 hours.

Josue must shovel at least 20 driveways.

The homeowner can use 5–20 hcf and still fall within the “conservation usage” billing range.

The homeowner can use 16–40 hcf and still fall within the “normal usage” billing range.

ⓐ ± 2 ± 2 ⓑ no solution ⓒ 0

ⓐ ± 11 ± 11 ⓑ no solution ⓒ 0

x = 4 , x = − 2 3 x = 4 , x = − 2 3

x = −1 , x = 5 2 x = −1 , x = 5 2

x = 8 , x = 0 x = 8 , x = 0

x = 8 , x = 2 x = 8 , x = 2

No solution

x = − 2 5 , x = − 2 5 , x = 5 2 x = 5 2

x = 3 , x = 3 , x = 1 9 x = 1 9

The diameter of the rod can be between 79.991 and 80.009 mm.

The diameter of the rod can be between 74.95 and 75.05 mm.

Section 2.1 Exercises

y = 5 y = 5

w = −18 w = −18

q = 3 q = 3

x = 14 x = 14

c = 4 c = 4

c = 5 2 c = 5 2

y = −5 y = −5

s = 10 s = 10

p = −4 p = −4

c = −4 c = −4

h = 3 4 h = 3 4

m = 6 m = 6

conditional equation; j = 2 5 j = 2 5

conditional equation; m = 16 5 m = 16 5

x = −1 x = −1

y = −1 y = −1

a = 3 4 a = 3 4

w = 9 4 w = 9 4

b = 12 b = 12

p = −41 p = −41

x = − 5 2 x = − 5 2

n = −3 n = −3

u = 3 u = 3

x = 18 x = 18

x = 20 x = 20

d = 8 d = 8

L = 19.75 L = 19.75 feet

Answers will vary.

Section 2.2 Exercises

58 hardback books

−11 , −12 , −13 −11 , −12 , −13

−69 , −71 , −73 −69 , −71 , −73

ⓐ 54 ⓑ 108 ⓐ 30%

ⓐ 162.5 162.5 ⓑ $35 ⓐ 150%

$ 11.88 $ 11.88

−2.5 % −2.5 %

−11 % −11 %

ⓐ $ 26.97 $ 26.97 ⓑ $ 17.98 $ 17.98

ⓐ $576 ⓑ 30%

ⓐ $ 7.20 $ 7.20 ⓑ $ 23.20 $ 23.20

ⓐ $ 0.20 $ 0.20 ⓑ $ 0.80 $ 0.80

3.75 % 3.75 %

21.2 % 21.2 %

Section 2.3 Exercises

d = C π d = C π

L = V W H L = V W H

d 1 = 2 A d 2 d 1 = 2 A d 2

b 1 = 2 A h − b 2 b 1 = 2 A h − b 2

a = 2 h − 108 t t 2 a = 2 h − 108 t t 2

a = 180 − b − c a = 180 − b − c

p = 2 A − 2 B l p = 2 A − 2 B l

L = P − 2 W 2 L = P − 2 W 2

y = 15 − 8 x y = 15 − 8 x

y = −6 + 4 x y = −6 + 4 x

y = 4 + x y = 4 + x

y = 7 − 4 x 3 y = 7 − 4 x 3

y = 12 − 2 x 3 y = 12 − 2 x 3

y = 18 − 3 x −2 y = 18 − 3 x −2

45 ° , 45 ° , 90 ° 45 ° , 45 ° , 90 °

30 ° , 60 ° , 90 ° 30 ° , 60 ° , 90 °

18 meters, 11 meters

13.5 13.5 m, 12.8 12.8 m

25 ft, 50 ft

12 ft, 13 ft, 14 ft

3 ft, 6 ft, 8 ft

120 yd, 160 yd

40 ft, 85 ft

104 ° F 104 ° F

ⓐ Answers will vary. ⓑ The areas are the same. The 2 × 8 2 × 8 rectangle has a larger perimeter than the 4 × 4 4 × 4 square. ⓒ Answers will vary.

Section 2.4 Exercises

nine nickels, 16 dimes

ten $10 bills, five $5 bills

63 dimes, 20 quarters

16 nickels, 12 dimes, seven quarters

330 day passes, 367 tournament passes

40 postcards, 100 stamps

15 $10 shares, five $12 shares

34 general, 61 youth

114 general, 246 student

Four pounds of macadamia nuts, eight pounds almonds

3.6 3.6 lbs Bermuda seed, 5.4 5.4 lbs Fescue seed

$33,000 in Fund A, $22,000 in Fund B

5.9 % 5.9 %

Kathy 5 mph, Cheryl 3 mph

commercial 550 mph, private plane 340 mph

Violet 65 mph, Charlie 55 mph

Ethan 22 mph, Leo 16 mph

DaMarcus 16 mph, Fabian 22 mph

uphill 1.6 1.6 mph, downhill 4.8 4.8 mph

light traffic 54 mph, heavy traffic 30 mph

freeway 67 mph, mountain road 22.3 mph

running eight mph, walking three mph

ⓐ 15 minutes ⓑ 20 minutes ⓒ one hour (d) 1:25

Section 2.5 Exercises

A maximum of 14 people can safely ride in the elevator.

five drinks

260 messages

62 necklaces

seven lawns

Section 2.6 Exercises

5 ≤ n ≤ 24 5 ≤ n ≤ 24

6 ≤ w ≤ 12 6 ≤ w ≤ 12

ⓐ answers vary ⓑ answers vary

Section 2.7 Exercises

ⓐ x = 4 , x = −4 x = 4 , x = −4 ⓑ no solution ⓒ z = 0 z = 0

ⓐ x = 3 , x = −3 x = 3 , x = −3 ⓑ no solution ⓒ z = 0 z = 0

x = 1 , x = − 1 2 x = 1 , x = − 1 2

x = −1 , x = − 5 2 x = −1 , x = − 5 2

x = 7 , x = 1 x = 7 , x = 1

x = 1 , x = −5 x = 1 , x = −5

no solution

x = −1 , x = − 2 3 x = −1 , x = − 2 3

x = −3 , x = 3 x = −3 , x = 3

x = 2 , x = 1 4 x = 2 , x = 1 4

x = 3 , x = 2 x = 3 , x = 2

x = 3 , x = − 11 3 x = 3 , x = − 11 3

x = 3 2 , x = − 1 2 x = 3 2 , x = − 1 2

The minimum to maximum expected production is 207,500 to 2,225,000 bottles

The acceptable weight is 22.5 to 25.5 ounces.

Review Exercises

s = −22 s = −22

m = −14 m = −14

q = 18 q = 18

k = 3 4 k = 3 4

k = 23 k = 23

x = 5 x = 5

There are 116 people.

−3 , −10 −3 , −10

$ 3.89 $ 3.89

ⓐ $105 ⓑ 52.5 % 52.5 %

d 2 = 2 A d 1 d 2 = 2 A d 1

y = 4 x 3 − 4 y = 4 x 3 − 4

22.5 ° , 67.5 ° , 90 ° 22.5 ° , 67.5 ° , 90 °

24.5 24.5 cm, 12.5 12.5 cm

9 ft, 14 ft, 12 ft

nine pennies, six dimes, 12 quarters

57 students, 68 general admission

2.2 2.2 lbs of raisins, 7.8 7.8 lbs of nuts

9.7 % 9.7 %

Louellen 65 mph, Tracy 66 mph

upstream 3 mph, downstream 5 mph

heavy traffic 32 mph, light traffic 68 mph

$33 per day

at least $300,000

at least 112 jobs

x = 2 , x = 2 3 x = 2 , x = 2 3

x = 9 , x = −3 x = 9 , x = −3

The minimum to maximum expected usage is 210,000 to 220,000 bottles

Practice Test

x = −5 x = −5

a = 41 a = 41

x = 6 x = 6

x = −2 , x = − 1 3 x = −2 , x = − 1 3

−57 , −55 −57 , −55

12 dimes, seven quarters

2.5 2.5 hours

At most $55.56 per costume.

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• Publication date: May 6, 2020
• Location: Houston, Texas
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Systems of Linear Equations Worksheets and Answer Keys

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Course: Algebra 1   >   Unit 5

• Slope-intercept equation from graph
• Writing slope-intercept equations
• Slope-intercept equation from slope & point
• Slope-intercept equation from two points
• Slope-intercept from two points
• Constructing linear equations from context

Writing linear equations word problems

• Slope-intercept form review

• List of Lessons
• 1.0 Marking the Text in Mathematics
• 1.1 Order of Operations
• 1.2 Translating Verbal Phrases
• 1.3 Functions as Rules and Tables
• 1.4 Functions as Graphs
• Unit 1 Review
• Unit 1 Skillz Review Help
• 2.1 Real Numbers
• 2.2 Add and Subtract Real Numbers
• 2.3 Multiply and Divide Real Numbers
• 2.4 Combine Like Terms and Distributive Property
• Unit 2 Review
• Unit 2 Skillz Review
• 3.1 One Step Equations
• 3.2 Two Step Equations
• 3.3 MultiStep Equations
• 3.4 Variables on Both Sides of the Equation
• Unit 3 Review
• 4.1 Ratios and Proportions
• 4.2 Solving Proportions using Cross Products
• 4.3 Solving Percent Problems
• 4.4 Solving for Y
• Unit 4 Shortcuts
• Unit 4 Review
• 5.1 Plot Points in a Coordinate Plane
• 5.2 Graphing Linear Equations and Using Intercepts
• 5.3 Slope and Rate of Change
• 5.4 Graph in Slope-Intercept Form
• 5.5 Graph Linear Functions
• Unit 5 Review
• 6.1 Write Equations in Slope Intercept Form
• 6.2 Use Equations in Slope Intercept Form
• 6.3 Equations in Parallel/Perpendicular Form
• 6.4 Fit Line To Data
• Unit 6 Review
• Unit 6 Skillz Review Help
• SEMESTER EXAM REVIEW
• 7.1 Inequalities
• 7.2 Solving Inequalities
• 7.3 Multi-step Inequalities
• 7.4 Absolute Value Equations
• 7.5 Linear Inequalities in Two Variables
• Unit 7 Skillz Review Help
• 8.1 Solving Systems by Graphing
• 8.2 Solving Systems using Substitution
• 8.3 Solving Systems using Elimination
• 8.4 Solving Special Case Systems
• 8.5 Solving Systems of Linear Inequalities
• Unit 8 Review
• 9.1 Expand and Condense Exponents
• 9.2 Exponent Rules
• 9.3 Zero and Negative Exponents
• 9.4 Scientific Notation
• Unit 9 Review
• 10.1 Add and Subtract Polynomials
• 10.2 Multiply Polynomials
• 10.3 Polynomial Equations in Factored Form
• 10.4 Factoring Trinomials
• 10.5 Solving Quadratics by Factoring
• 10.6 Double Factoring
• Unit 10 Review
• Unit 10 Skillz Review Help
• 11.1 Simplifying Radicals
• 11.2 Operations with Square Roots
• Unit 11 Review
• 12.1 Graphing Quadratics
• 12.2 Solve Quadratics by Graphing
• 12.3 Solve Quadratics Using Square Roots
• 12.4 Solve Quadratics Using the Quadratic Formula
• Unit 12 Review
• Unit 12 Skillz Review
• SEMESTER 2 EXAM REVIEW
• Teacher Resources
• Flippedmath.com

Section 6.1 Write Equations in Slope Intercept Form

Practice Solutions

Corrective Assignment

Application walkthrough.

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3.6 Write Linear Equations

Mathematics.

10 questions

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• 1. Multiple Choice Edit 3 minutes 1 pt What does the "b" stand for in y=mx+b? slope x-intercept y-intercept
• 2. Multiple Choice Edit 3 minutes 1 pt What is the equation for the line that passes through the points (4,2) and (0,6)? y = x + 6 y = -2x + 2 y = -x - 6 y = -x + 6
• 3. Multiple Choice Edit 3 minutes 1 pt What is the y-intercept in the equation? y = 5x - 4 5 -4 -5 4

Write the equation of the line that passes through the point (1, -1) and has a slope of -4.

y = -4x + 3

y = -4x - 3

y = -4x + 5

y = -4x - 5

• 6. Multiple Choice Edit 3 minutes 1 pt What is an equation for the line that passes through the coordinates (-1,2) and (7,6)  ? y = (1/2)x + 2.5 y = (1/2)x - 5 y = 3x + 4 y = -3x + 4
• 7. Multiple Choice Edit 3 minutes 1 pt Write an equation in slope-intercept form from the points (-4, 0) and (1, 5) y = x - 4 y = x + 4 x = y + 4 y = 4x + 4

Write an equation in slope-intercept form from the points (0, 5) and (4, 3)

y = 1/2x + 5

y = 1/2x - 5

• 10. Multiple Choice Edit 3 minutes 1 pt Paul the plumber charges $25 for a service call.  He then charges $100 an hour.  Write a linear equation to model this situation. y = 100x y = 25x y = 25x + 100 y = 100x + 25

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