# Ch 2: Common Core HS Algebra: Linear Equations

### About This Chapter

**Standard:** Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. (CCSS.Math.Content.HSA-REI.A.1)

**Standard:** Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. (CCSS.Math.Content.HSA-REI.B.3)

**Standard:** Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). (CCSS.Math.Content.HSA-REI.D.10)

**Standard:** Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. (CCSS.Math.Content.HSA-CED.A.1)

**Standard:** Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. (CCSS.Math.Content.HSA-CED.A.2)

**Standard:** Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. (CCSS.Math.Content.HSA-CED.A.4)

## About This Chapter

Students who have mastered these standards are able to explain and write linear equations. When working with linear equations, they will be able to solve them with or without letter coefficients.

Lessons in this standard cover concepts such as:

- Using linear equations to solve problems
- Solving problems with implicit equations
- Graphing linear equations
- Representing undefined and zero slopes on a graph

Students demonstrate mastery of this standard when working with and identifying the different parts of a graph when charting linear equations. Mastery of this standard supports their career and education because linear equations are found in many aspects of algebra. Linear equations can be used to help predict real life patterns.

### How to Use These Lessons in Your Classroom

Here are some tips for how to use the lessons to support instruction in these standards:

#### Graph Parts Identification Lessons

Create a worksheet that has a graph and blank labels pointing to different parts of a graph. Exhibit the video lesson 'What are the Different Parts of a Graph?' Have the students fill the graph worksheet out while they're watching the video.

#### Writing Linear Equations Lessons

Develop a worksheet with questions that provides your students with enough information to assemble linear equations. After passing out the worksheet, watch the video 'How to Write a Linear Equation.' Separate the students into groups of 2 or 3. Allow your students to have time to complete the worksheet. Call on students to write their results on the board.

#### Graphing Linear Equations

After your students complete the previous exercise, have them watch the 'Linear Equations: Intercepts, Standard Form and Graphing' video lesson. Provide the groups with graph paper and assign each group a linear equation to use. When each group has completed graphing their linear equation, discuss the results and collect each group's graphing sheet.

### 1. What Are the Different Parts of a Graph?

Being able to read a graph isn't just vital for an algebra class. Graphs and charts are used everywhere! We'll take a crash course on the basic x/y plane used in algebra and the fundamental vocab you need.

### 2. What is a Linear Equation?

Most cars won't be able to run for more than 250,000 miles, so how much longer will your car live? Linear Equations are the most basic kind of algebraic function and can help you answer questions exactly like this. Learn about what they look like, how they come up in your life and why they are powerful tools.

### 3. Linear Equations: Intercepts, Standard Form and Graphing

Do you know what to do if an equation doesn't look like y=mx+b?! If not, then this video is for you. Chances are the equation is in standard form, so we'll learn how to use standard form equations, how to graph them and why they can be helpful.

### 4. Abstract Algebraic Examples and Going from a Graph to a Rule

Just because you now know what a linear equation is doesn't mean that you are a master! This video will help you learn how to apply your knowledge of linear equations in more abstract algebraic ways.

### 5. Graphing Undefined Slope, Zero Slope and More

There are two special cases when it comes to slopes on the xy plane: horizontal and vertical lines. Without any more information, these examples can be pretty confusing. But with a little instruction, they end up being some of the easiest lines to graph!

### 6. How to Write a Linear Equation

Simply knowing how to take a linear equation and graph it is only half of the battle. You should also be able to come up with the equation if you're given the right information.

### 7. Solving Linear Equations: Practice Problems

With practice, linear equations can be straightforward to solve. In this lesson, we'll define linear equations and learn how to solve them. We'll look at multiple practice problems and walk through solving each one.

### 8. Solving Linear Equations with Literal Coefficients

In this lesson, we'll literally learn about literal coefficients. We'll look at how to solve linear equations that contain literal coefficients and practice solving several problems.

### 9. Problem solving using Linear Equations

From sale prices to trip distances, many real life problems can be solved using linear equations. In this lesson, we'll practice translating word problems into linear equations, then solving the problems.

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### Other Chapters

Other chapters within the Common Core Math - Algebra: High School Standards course

- Common Core HS Algebra: Algebraic Expressions
- Common Core HS Algebra: Linear Inequalities
- Common Core HS Algebra: Quadratics
- Common Core HS Algebra: Exponents and Exponential Functions
- Common Core HS Algebra: Polynomials
- Common Core HS Algebra: Rational and Radical Expressions and Equations
- Common Core HS Algebra: Systems of Equations
- Common Core HS Algebra: Matrices
- Common Core HS Algebra: Sequences and Series
- Understanding Common Core Standards