About This Chapter
Working with Linear Equations - Chapter Summary and Learning Objectives
Explore how linear equations can be used to chart variables that increase or decrease at a constant rate with the lessons included in this chapter. Instructors show you how to use x- and y-coordinates and slope to write and graph these types of equations. By the time you finish this chapter, you should be able to:
- Solve and graph linear equations
- Identify graphs with zero and undefined slope
- Recognize the equations of two parallel or perpendicular lines
- Write linear equations in standard and slope-intercept forms
|What Is a Linear Equation?||Reacquaint yourself with the slope-intercept form of a linear equation and its graph.|
|Applying the Distributive Property to Linear Equations||Learn how the distributive property can be used to solve a linear equation.|
|Linear Equations: Intercepts, Standard Form and Graphing||Find out how to convert a linear equation into standard form and graph it.|
|Abstract Algebraic Examples and Going from a Graph to a Rule||Practice using a graph's slope or position on the coordinate plane to identify its equation.|
|Graphing Undefined Slope, Zero Slope and More||Identify lines with zero and undefined slope by examining their graphs or the values represented in their equations.|
|Graphs of Parallel and Perpendicular Lines in Linear Equations||Examine the equations of two lines to determine if they're parallel or perpendicular.|
|How to Write a Linear Equation||Practice writing linear equations when given two points or the equation of a parallel or perpendicular line.|
|Equation of a Line Using Point-Slope Formula||Get instruction on the steps required to write a linear equation using the point-slope formula.|
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. 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.
7. 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.
8. Equation of a Line Using Point-Slope Formula
It's time for a road trip to Las Vegas, and after four hours of driving at 60 mph ... Are we there yet? Learn the point-slope form of the equation of a line to help answer this age-old question.
9. Understanding Numbers That Are Pythagorean Triples
In this video lesson, you will learn about numbers that form Pythagorean Triples. Learn why these are special numbers and what they have to do with triangles.
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Other chapters within the Fundamental Trigonometry course
- Real Numbers: Types and Properties
- Working With Inequalities
- Absolute Value Equations
- Working with Complex Numbers
- Systems of Linear Equations
- Mathematical Modeling
- Introduction to Quadratics
- Working with Quadratic Functions
- Coordinate Geometry Review
- Functions for Trigonometry
- Understanding Function Operations
- Graph Symmetry
- Graphing with Functions
- Polynomial Functions Basics
- Higher-Degree Polynomial Functions
- Rational Functions & Difference Quotients
- Rational Expressions and Function Graphs
- Exponential Functions & Logarithmic Functions
- Using Trigonometric Functions
- Triangle Trigonometry
- Trigonometric Graphs
- Solving Trigonometric Equations
- Trigonometric Identities
- Trigonometric Applications
- Analytic Geometry and Conic Sections
- Vectors, Matrices and Determinants
- Polar Coordinates and Parameterizations
- Circular Arcs, Circles & Angles