lesson 8 homework practice write linear equations

Chapter 8, Lesson 8: Writing Linear Equations

• Extra Examples
• Personal Tutor
• Self-Check Quizzes

The resource you requested requires you to enter a username and password below:

Please read our Terms of Use and Privacy Notice before you explore our Web site. To report a technical problem with this Web site, please contact the site producer .

You are using an outdated browser and it's not supported. Please upgrade your browser to improve your experience.

• LOGIN FOR PROGRAM PARTICIPANTS
• PROGRAM SUPPORT

Writing and Solving Linear Equations

Description.

In Topic A, students begin by transcribing written statements using symbolic notation. Then, students write linear and non-linear expressions leading to linear equations, which are solved using properties of equality.

Students learn that not every linear equation has a solution. In doing so, students learn how to transform given equations into simpler forms until an equivalent equation results in a unique solution, no solution, or infinitely many solutions. Throughout Topic A students must write and solve linear equations in real-world and mathematical situations.

There may be cases when our downloadable resources contain hyperlinks to other websites. These hyperlinks lead to websites published or operated by third parties. UnboundEd and EngageNY are not responsible for the content, availability, or privacy policies of these websites.

• Grade 8 Mathematics Module 4, Topic A, Overview
• CCSS Standard:

In This Unit

• lesson 1: Writing Equations Using Symbols
• lesson 2: Linear and Nonlinear Expressions in x
• lesson 3: Linear Equations in x
• lesson 4: Solving a Linear Equation
• lesson 5: Writing and Solving Linear Equations
• lesson 6: Solutions of a Linear Equation
• lesson 7: Classification of Solutions
• lesson 8: Linear Equations in Disguise
• lesson 9: An Application of Linear Equations

Related Guides and Multimedia

Our professional learning resources include teaching guides, videos, and podcasts that build educators' knowledge of content related to the standards and their application in the classroom.

There are no related guides or videos. To see all our guides, please visit the Enhance Instruction section here .

• Notifications 0

• Add Friend ($5)

As a registered member you can:

• View all solutions for free
• Request more in-depth explanations for free
• Ask our tutors any math-related question for free
• Email your homework to your parent or tutor for free
• Grade 8 HMH Go Math - Answer Keys

Explanation:

b. output variable:

c. equation:

• Type below:

Kate is planning a trip to the beach. She estimates her average speed to graph her expected progress on the trip. Write an equation in slope-intercept form that represents the situation. 

At 59 °F, crickets chirp at a rate of 76 times per minute, and at 65 °F, they chirp 100 times per minute. Write an equation in slope-intercept form that represents the situation.

  Essential Question Check-In  

Explain what m and b in the equation \(\text{y} = \text{mx + b}\) tell you about the graph of the line with that equation.

Yes, email page to my online tutor. ( if you didn't add a tutor yet, you can add one here )

Thank you for doing your homework!

Submit Your Question

Curriculum  /  Math  /  7th Grade  /  Unit 3: Numerical and Algebraic Expressions  /  Lesson 8

Numerical and Algebraic Expressions

Lesson 8 of 11

Criteria for Success

Tips for teachers, anchor problems, problem set, target task, additional practice.

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 2).

Common Core Standards

Core standards.

The core standards covered in this lesson

Expressions and Equations

7.EE.A.1 — Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Foundational Standards

The foundational standards covered in this lesson

6.EE.A.3 — Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

6.EE.A.4 — Identify when two expressions are equivalent (i.e., when the two expressions name the same number regardless of which value is substituted into them). For example, the expressions y + y + y and 3y are equivalent because they name the same number regardless of which number y stands for.

The Number System

7.NS.A.1 — Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

7.NS.A.2 — Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

The essential concepts students need to demonstrate or understand to achieve the lesson objective

• Look for and make use of structure in expressions (MP.7).
• Analyze student work to understand different approaches in simplifying expressions.
• Simplify expressions involving adding, subtracting, and expanding expressions with rational numbers.

Suggestions for teachers to help them teach this lesson

The numbers used in the problems in this lesson require skills working with positive and negative rational numbers. This is a good opportunity to spiral in skills from the previous unit aligned to 7.NS.1 and 7.NS.2. Resources in the Problem Set Guidance include a range of problems from simpler, with just integers, to more complex, with fractions and decimals. Students should get exposure to a wide range of difficulty levels.

Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.

Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding

A student simplified the expression below as part of their homework. Review their work and check for any mistakes. For each line in their work, explain what they did to get their next step.

Homework Problem:

$${-\frac{1}{3}(5x-2y)-2\left ( \frac{1}{2}x+\frac{1}{3}y \right )}$$

Student’s Work:

Step 1:  $${-\frac{5}{3}x+\frac{2}{3}y-x-\frac{2}{3}y}$$

Step 2:  $${-\frac{5}{3}x-x+\frac{2}{3}y-\frac{2}{3}y}$$

Step 3:  $${\left ( -\frac{5}{3}-1 \right )x+0}$$

Step 4:  $${-\frac{8}{3}x}$$

Guiding Questions

Find the perimeter of the parallelogram.

An expression is given.

$${-2y+\frac{3}{2}x+\frac{7}{4}}$$

Which are equivalent to the given expression? Select each correct answer.

Math Spring Operational 2016 Grade 7 Released Items is made available by The Partnership for Assessment of Readiness for College and Careers (PARCC) . Copyright © 2017 All Rights Reserved. Accessed Oct. 9, 2017, 10:59 a.m..

A set of suggested resources or problem types that teachers can turn into a problem set

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved

Which expressions are equivalent to the expression $$n+\frac{5}{6}(m-n)-\frac{1}{3}m$$ ? Select all that apply.

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

• Have students swap work every now and then to check and correct each other’s work (without an answer key). 
• Kuta Software Free Algebra 1 Worksheets Basics - Combining Like Terms
• Utah Middle School Math Project Chapter 3 Expressions and Equations Student Workbook — pages 60 - 62, 64, 65
• PARCC Released Items Math Spring Operational 2016 Grade 7 Released Items — Problem 16
• PARCC Released Items Math Spring Operational 2015 Grade 7 End of Year Released Items — Problem 4

Topic A: Evaluating Numerical and Algebraic Expressions

Evaluate numerical expressions with rational numbers using the order of operations.

7.EE.A.1 7.NS.A.3

Write and evaluate expressions for mathematical and contextual situations.

Create a free account to access thousands of lesson plans.

Already have an account? Sign In

Topic B: Generating Equivalent Expressions

Expand and factor expressions using the distributive property and the greatest common factor.

Expand and factor expressions with negative rational numbers.

Add and simplify expressions by combining like terms.

Subtract and simplify expressions.

Simplify expressions by combining like terms and using the distributive property and properties of operations (Part 1).

Write and interpret expressions in different ways to shed new meaning on a context.

Topic C: Solving Multi-Step Problems using Expressions

Solve multi-step real-world problems with rational numbers.

7.EE.B.3 7.NS.A.3

Model real-world problems involving rational numbers using reasoned estimates.

Request a Demo

See all of the features of Fishtank in action and begin the conversation about adoption.

Learn more about Fishtank Learning School Adoption.

Contact Information

School information, what courses are you interested in, are you interested in onboarding professional learning for your teachers and instructional leaders, any other information you would like to provide about your school.

Effective Instruction Made Easy

Access rigorous, relevant, and adaptable math lesson plans for free

If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

Unit 4: Systems of linear equations

Writing & graphing systems of linear equations.

• Systems of equations: trolls, tolls (1 of 2) (Opens a modal)
• Systems of equations: trolls, tolls (2 of 2) (Opens a modal)
• Testing a solution to a system of equations (Opens a modal)
• Systems of equations with graphing: y=7/5x-5 & y=3/5x-1 (Opens a modal)
• Systems of equations with graphing: exact & approximate solutions (Opens a modal)
• Setting up a system of equations from context example (pet weights) (Opens a modal)
• Setting up a system of linear equations example (weight and price) (Opens a modal)
• Interpreting points in context of graphs of systems (Opens a modal)
• Solutions of systems of equations Get 3 of 4 questions to level up!
• Systems of equations with graphing Get 3 of 4 questions to level up!
• Creating systems in context Get 3 of 4 questions to level up!
• Interpret points relative to a system Get 3 of 4 questions to level up!

Solving systems by substitution

• Systems of equations with substitution: potato chips (Opens a modal)
• Systems of equations with substitution: -3x-4y=-2 & y=2x-5 (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!

Solving systems by elimination (part 1)

• Why can we subtract one equation from the other in a system of equations? (Opens a modal)
• Worked example: equivalent systems of equations (Opens a modal)
• Worked example: non-equivalent systems of equations (Opens a modal)
• Reasoning with systems of equations (Opens a modal)
• Equivalent systems of equations review (Opens a modal)
• Reasoning with systems of equations Get 3 of 4 questions to level up!

Solving systems by elimination (part 2)

• Systems of equations with elimination: King's cupcakes (Opens a modal)
• Systems of equations with elimination: x-4y=-18 & -x+3y=11 (Opens a modal)
• Systems of equations with elimination Get 3 of 4 questions to level up!

Solving systems by elimination (part 3)

• Elimination strategies (Opens a modal)
• Systems of equations with elimination: potato chips (Opens a modal)
• Systems of equations with elimination (and manipulation) (Opens a modal)
• Elimination method review (systems of linear equations) (Opens a modal)
• Elimination strategies Get 3 of 4 questions to level up!
• Systems of equations with elimination challenge Get 3 of 4 questions to level up!

Systems of linear equations and their solutions

• Systems of equations number of solutions: fruit prices (1 of 2) (Opens a modal)
• Systems of equations number of solutions: fruit prices (2 of 2) (Opens a modal)
• Solutions to systems of equations: consistent vs. inconsistent (Opens a modal)
• Solutions to systems of equations: dependent vs. independent (Opens a modal)
• Number of solutions to a system of equations (Opens a modal)
• Number of solutions to a system of equations graphically (Opens a modal)
• Number of solutions to a system of equations algebraically (Opens a modal)
• How many solutions does a system of linear equations have if there are at least two? (Opens a modal)
• Number of solutions to system of equations review (Opens a modal)
• Number of solutions to a system of equations graphically Get 3 of 4 questions to level up!
• Number of solutions to a system of equations algebraically Get 3 of 4 questions to level up!

Chapter 8, Lesson 8: Writing Linear Equations

• Extra Examples
• Personal Tutor
• Self-Check Quizzes

The resource you requested requires you to enter a username and password below:

Please read our Terms of Use and Privacy Notice before you explore our Web site. To report a technical problem with this Web site, please contact the site producer .