About This Chapter
Understanding & Solving Linear Functions - Chapter Summary
By going through this chapter, you can review the process involved in understanding and solving linear functions. Our instructors go over the connections among linear functions, equations, and the graphing process, providing you with a thorough overview of all the necessary steps involved. These lessons cover basic formulas and show you practical applications for these types of functions and equations. After you take some time to look at this chapter, you should feel ready to do the following:
- Describe a linear function
- Identify the steps for writing a linear equation
- Analyze graphing, standard form, and intercepts
- Define the slope of a line and how to find it
- Compare graphing zero slope, undefined slope, and more
- Examine the point-slope formula and the equation of a line
- Explain the process for writing and reviewing real-life linear models
It may have been a long time since you have reviewed these fundamental linear functions concepts, so you may not recall all the details. Fortunately, our instructors understand where you are coming from, and they have designed this chapter to give you the type of help you need. For example, the chapter is divided into individual lessons, all of which are clearly labeled. This way you can navigate yourself through our chapter to the lessons you need to review the most and skip over topics you already know.
1. What is a Linear Function? - Definition & Examples
In this lesson, you will learn the key identifying mark of linear functions. You'll also learn how to graph them with just two points and how you can use the graph to easily find your answers.
2. Linear and Nonlinear Functions
After watching this video lesson, you'll be able to tell the differences between linear and nonlinear functions. You'll also be able to identify both types just by looking at graphs.
3. 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.
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. How to Find and Apply The Slope of a Line
In this lesson, we'll discover all about the slopes of lines. We'll learn about different types of slopes and how to find the slopes of lines. We'll use two methods: the slope formula and the slope-intercept form.
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. 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.
8. Writing & Evaluating Real-Life Linear Models: Process & Examples
You make decisions about budgeting and other financial issues using linear models without even realizing it. Learn how to write and evaluate linear models.
9. Determine the Rate of Change of a Function
In this lesson, we will learn about the rate of change of a function with specific focus on linear and exponential functions while examining the graphs of both types of functions.
10. Connections Among Proportional Relationships, Lines & Linear Equations
Proportional relationships in mathematics happen when two values always change by the same multiple. If one doubles, the other doubles. This lesson will discuss the connection among proportional relationships, lines, and linear equations.
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Other chapters within the MTEL General Curriculum (03): Practice & Study Guide course
- History of the English Language
- Basic Grammar & Mechanics
- Teaching Literature & Literary Analysis
- Literary Genres
- Literary Elements & Concepts
- Children's Literature Genres & Characteristics
- The Writing Process
- Writing Styles & Techniques
- Paleolithic Era to the Agricultural Revolution
- Early Civilizations & the Rise of Western Imperialism
- Modern World History Overview
- The Start of the United States
- American History 1800 to 1900
- American History 1900 to 1950
- American History 1950 to Present Day
- US & Massachusetts Government
- Fundamentals of Economics & Capitalism
- Geography & Human Settlements
- Principles of Life Sciences
- Principles of Physical Science
- Earth & Space Science
- Foundations of Scientific Thought
- Scientific Inquiry & Experimentation
- The Number System
- Fractions, Decimals & Percents Overview
- Factoring & Divisibility Rules
- Number Operations
- Basic Algebraic Concepts & Practice
- Introduction to Functions & Graphs
- Concepts of Measurement
- Geometric Shapes & Principles
- Understanding Descriptive Statistics
- Understanding Probability
- MTEL General Curriculum Flashcards