About This Chapter
When learning algebra, it's important to develop a solid understanding of its foundations. In these videos, you'll learn basic algebra concepts, such as the different types of numbers (natural, whole, integers, rational, irrational and real), as well as the fundamentals of graphing. You'll learn the different parts of the graph, which is also known as the Cartesian plane. These basic parts include the x and y-axes, four quadrants, the x and y-intercepts and ordered pairs.
Next, you'll focus on an important and common aspect of algebra known as linear equations. Linear equations are patterns of numbers that either increase or decrease by the same amount, and when graphed, they form (you guessed it) straight lines. You'll also find out some of the practical uses of linear equations. These include understanding and predicting patterns in real life, such as how many years you can expect your car to travel before it dies. Slope-intercept form and standard form help you graph and solve linear equations.
Later, you'll build on your graphing and linear equation skills by learning how to graph undefined slopes and zero slopes, go from a graph to a rule and solve more abstract algebra problems.
Building on linear equations, you'll become familiar with systems of equations and learn how to graph and apply them to real life. These videos can help you understand the practical uses of systems of equations, how to identify variables from word problems and how to perform substitution and elimination methods.
1. What are the Different Types of Numbers?
Learn all of the different types of numbers: natural numbers, whole numbers, integers, rational numbers, irrational numbers, and real numbers. This video lesson teaches you how to classify any numbers you come across.
2. 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.
3. 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.
4. 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.
5. 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.
6. 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!
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. 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.
9. 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.
10. Practice Problem Set for Foundations of Linear Equations
If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.
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Other chapters within the Math 101: College Algebra course
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Rational Expressions
- Radical Expressions & Functions
- Exponentials and Logarithms
- Probability Mechanics
- Sequences and Series
- Studying for Math 101