# Ch 12: High School Algebra: Linear Equations

### About This Chapter

## High School Algebra: Linear Equations - Chapter Summary

Believe it or not, we use algebra throughout our daily routines, including when we cook, when we make our schedules, and even when we go shopping, so having a basic comprehension of algebraic formulas could help you make better real-life decisions. In these lessons, you will find out about linear equations, including the purpose of these equations, how to write them, graphing procedures, and more.

To make sure you understand this topic, try answering the questions on the lesson quizzes. Most of our quizzes include at least five selected-response questions, and you will have to know specific information about any given topic, such as definitions, formulas, concept applications, and terminology. Our quizzes are available around the clock online, and you have the option to print the quiz worksheets. Upon completing this chapter, you will have the ability to do the following:

- Describe a linear equation and a system of equations
- Identify how the distributive property of linear equations is applied
- Analyze the graphing, standard form, and intercepts of linear equations
- Check out examples about abstract algebraic equations
- Graph zero-slope or undefined-slope linear equations
- Define transverse, perpendicular, and parallel lines
- Compare linear equation graphs for perpendicular and parallel lines
- Practice writing linear equations
- Show the practical applications for a system of equations

### 1. 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.

### 2. Applying the Distributive Property to Linear Equations

When it comes to linear equations, there are certain steps you have to take to solve them. One of them is the application of the distributive property when you see a pair of parentheses. Watch this video lesson to learn how.

### 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. Parallel, Perpendicular and Transverse Lines

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

### 7. Graphs of Parallel and Perpendicular Lines in Linear Equations

When we deal with linear equations, we sometimes come across equations that are parallel to each other or perpendicular to each other. You will see what they look like when graphed in this video lesson.

### 8. 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.

### 9. What is a System of Equations?

So what happens if we want to compare more than one equation? Welcome to a 'system' of equations! Learn what one is, how to solve them and when they come up in real life.

### 10. How Do I Use a System of Equations?

There are a few classic algebra word problems, such as the one about two trains traveling at different speeds. In this lesson, you'll learn how to take a word problem and convert it into the system of equations that will allow you to find the answer using either substitution or elimination.

### 11. Nonlinear Function: Definition & Examples

In this lesson, we will familiarize ourselves with linear functions in order to define and understand what nonlinear functions are. We will become comfortable determining if a function is linear or nonlinear through definitions and examples.

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### Other Chapters

Other chapters within the Algebra I: High School course

- High School Algebra: Solving Math Word Problems
- High School Algebra: Percent Notation
- High School Algebra: Calculations, Ratios, Percent & Proportions
- High School Algebra: Real Numbers
- High School Algebra: Exponents and Exponential Expressions
- High School Algebra: Properties of Exponents
- High School Algebra: Radical Expressions
- High School Algebra: Algebraic Expressions and Equations
- High School Algebra: Algebraic Distribution
- High School Algebra: Properties of Functions
- High School Algebra: Working With Inequalities
- High School Algebra: Factoring
- High School Algebra: Quadratic Equations
- High School Algebra: Graphing and Factoring Quadratic Equations
- High School Algebra: Properties of Polynomial Functions
- High School Algebra: Rational Expressions
- High School Algebra: Matrices and Absolute Value
- High School Algebra: Data, Statistics, and Probability