About This Chapter
Linear Equations and Inequalities - Chapter Summary and Learning Objectives
The lessons in this chapter explore linear equations and inequalities. You'll examine various types of graphing, such as graphing undefined slope, and get practice in creating graphs. Other lessons cover systems of equations and how they are used. At the end of this chapter, you should be able to:
- Recognize a linear equation
- Write a linear equation
- Graph an undefined and zero slope
- Graph one- and two-variable inequalities
- Understand and utilize a system of equations
|What is a Linear Equation?||Recognize a linear equation.|
|Linear Equations: Intercepts, Standard Form and Graphing||Put linear equations into standard form and create graphs depicting linear equations.|
|Abstract Algebraic Examples and Going from a Graph to a Rule||Learn to work with abstract algebraic examples and learn to convert an equation from a graph to a rule.|
|Graphing Undefined Slope, Zero Slope and More||Create graphs showing undefined and zero slope.|
|How to Write a Linear Equation||Learn to write a linear equation.|
|Equation of a Line Using Point-Slope Formula||Use point-slope formula to depict the equation of a line.|
|What is an Inequality?||Identify and understand inequalities.|
|How to Graph 1- and 2-Variable Inequalities||Learn to graph 1- and 2-variable inequalities.|
|Graphing Inequalties: Practice Problems||Practice graphing inequalities.|
|What is a System of Equations?||Understand a system of equations.|
|How Do I Use a System of Equations?||Learn to use 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. 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.
3. 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.
4. 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!
5. 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.
6. 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.
7. What is an Inequality?
Deciding how to spend your money can be a tricky thing. Should you save it, invest it, or enjoy it? Learn how inequalities can help you make your decision!
8. How to Graph 1- and 2-Variable Inequalities
So an inequality is just an equation with a less than or greater than symbol. But what is the difference between 1 and 2 variable inequalities? What does have a greater than or equal to symbol change? When do you use a number line instead of a coordinate plane? Get those answers here!
9. Graphing Inequalities: Practice Problems
If you're already pretty familiar with what inequalities are and just looking for a place to practice your skills, this is the place. This lesson covers topics like 1-variable, 2-variable, compound, and systems of inequalities.
10. 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.
11. 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.
12. System of Equations Word Problem Examples
Most word problems require that you find the value of one variable. But, what if there is more than one unknown variable? In this lesson, you'll use systems of equations and solve word problems that have more than one unknown value.
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Other chapters within the Math 105: Precalculus Algebra course
- Mathematical Modeling
- Quadratic Functions
- Rational Expressions and Functions
- Polynomial Functions of a Higher Degree
- Absolute Value Equations & Inequalities
- Complex Numbers
- Geometry Basics
- Functions Overview
- Function Operations
- Graph Symmetry
- Exponential and Logarithmic Functions
- Introduction to the Derivative
- Studying for Math 105