# Ch 12: Honors Algebra 2: Linear Equations

### About This Chapter

## Honors Algebra 2: Linear Equations - Chapter Summary and Learning Objectives

Honors Algebra 2 is designed to present new math challenges that can carry you into your studies at a college or university. Feel good about your ability to comprehend course concepts and earn high grades by taking advantage of the resources in this chapter. Lessons help you better understand linear equations by exploring related definitions, explanations and examples. You'll learn the meaning of the linear equation, how to apply properties, graph lines and write a linear equation.

The key to getting the most out of this chapter is utilizing as many resources as possible. Review the lessons as entertaining videos, or access full transcripts with vocabulary words that can strengthen your understanding of linear equations. Access the lessons from your home computer or on the go via you smartphone or tablet. Gauge your comprehension of the subject area by taking short quizzes and a chapter exam, and have any lesson questions answered by our experts. In no time, you will understand:

- The meaning of the linear equation and how to apply the distributive property to linear equations
- Linear equations as related to intercepts, standard form and graphs
- Abstract algebra and going from a graph to a rule
- The basics of parallel, perpendicular and transverse lines
- Graphs of parallel and perpendicular lines and how to write a linear equation

Video | Objective |
---|---|

What is a Linear Equation? | Learn the basic definition of a linear equation, what it looks like, how it makes appearances in your life and why it is a powerful tool. |

Applying the Distributive Property to Linear Equations | Describe how to solve linear equations with parentheses by applying the distributive property. |

Linear Equations: Intercepts, Standard Form and Graphing | Understand how to recognize when an equation is in standard form and how to use and graph standard form equations. |

Abstract Algebraic Examples and Going from a Graph to a Rule | Examine linear equations in abstract algebraic ways. |

Parallel, Perpendicular and Transverse Lines | Identify different types of lines, and explain where they are visible in the real world and how to recognize them. |

Graphs of Parallel and Perpendicular Lines in Linear Equations | See what equations look like when parallel or perpendicular to each other and graphed. |

How to Write a Linear Equation | Discover the steps involved in writing a linear equation. |

### 1. What is a Linear Equation?

A linear equation is a pattern of numbers with proportional increase or decrease that is used to represent a line graph. Learn how to plot a graph and build and solve a linear equation.

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

In mathematics, the distributive property shows that the same answer will result whether one number is multiplied by each integer in a group of numbers or by the sum of the group of numbers. Learn about applying the distributive property to linear equations and work examples to practice the steps, including the final steps needed to solve the equations.

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

To solve a linear equation, begin by determining whether it is written in the standard form or the slope-intercept form. Explore the differences between the slope-intercept form and the standard form of a linear equation, and learn how to graph the point of intercept for each.

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

Abstract algebraic concepts are often difficult to understand because they do not include many numbers but are mostly variables and letters. Learn more about abstract algebraic concepts, finding the equation on a graph, identifying graphs by appearance, and finding the greatest slope on a graph.

### 5. Parallel, Perpendicular and Transverse Lines

Lines have a specific shape, but there are different types of them according to how they relate to other lines in the same plane. Learn about the different types of lines, including parallel, perpendicular, and transverse lines, and see the formulas you can use to determine the type of line.

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

Linear equations, which are graphed as straight lines, can have associated parallel lines which never touch, and perpendicular lines that intersect at 90 degrees. Learn the equations and see the graphs of these two types of linear equations.

### 7. How to Write a Linear Equation

Rather than drawing a graph from an equation, graphs can be used to determine equations using common algebraic techniques. Learn how to write a linear equation using two points and the slope formula as well as using background information on parallel and perpendicular lines.

### Earning College Credit

Did you know… We have over 220 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Other Chapters

Other chapters within the Honors Algebra 2 Textbook course

- Honors Algebra 2: Basic Arithmetic Review
- Honors Algebra 2: Fractions Review
- Honors Algebra 2: Statistics
- Honors Algebra 2: Algebraic Expressions
- Honors Algebra 2: Solving Algebraic Equations
- Honors Algebra 2: Properties of Real Numbers
- Algebra II: Complex and Imaginary Numbers
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Absolute Value Review
- Honors Algebra 2: Properties of Functions
- Honors Algebra 2: Graphing Functions
- Honors Algebra 2: Graphing Linear Equations
- Honors Algebra 2: Graphing & Interpreting Scatterplots
- Honors Algebra 2: Systems of Linear Equations
- Honors Algebra 2: Solving & Graphing Linear Inequalities
- Algebra II: Matrices and Determinants
- Honors Algebra 2: Polynomials
- Honors Algebra 2: Graphing Polynomials
- Algebra II: Factoring
- Honors Algebra 2: Roots of Real Numbers
- Honors Algebra 2: Radical Expressions
- Honors Algebra 2: Solving Rational Expressions
- Honors Algebra 2: Quadratic Formula
- Honors Algebra 2: Graphing, Solving & Factoring Quadratic Equations
- Algebra II: Exponential and Logarithmic Functions
- Algebra II: Sets
- Algebra II: Combinatorics Review
- Honors Algebra 2: Trigonometric Functions
- Honors Algebra 2: Trigonometric Graphs
- Honors Algebra 2: Trigonometric Applications
- Honors Algebra 2: Solving Trigonometric Equations
- Honors Algebra 2: Trigonometric Identities
- Honors Algebra 2: Circles, Angles & Circular Arcs
- Algebra II: Conic Sections
- Algebra II: Sequences and Series
- Honors Algebra 2: Calculations, Ratios, Percent & Proportions