# Ch 4: Explorations in Core Math Algebra 1 Chapter 4: Linear Functions

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Linear Functions chapter of your textbook.
- Watch fun videos that cover the linear functions concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Discrete and continuous functions
- Function tables
- Linear equations
- Graphing undefined and zero slopes
- Determining rate of change
- Estimating slope
- Direct and inverse variations
- Graphing absolute values
- Writing and graphing linear functions
- Using a system of equations
- Calculating slopes
- Formulas for standard form
- Residual plots
- Using linear regression
- Transforming functions

*Explorations in Core Math is a registered trademark of Houghton Mifflin Harcourt, which is not affiliated with Study.com.*

### 1. Discrete & Continuous Functions: Definition & Examples

After this lesson, you will understand the differences between discrete functions and continuous functions. You'll learn the one criterion that you need to look at to determine whether a function is discrete or not.

### 2. Function Table in Math: Definition, Rules & Examples

Functions can be represented in four different ways. In this lesson, we will learn what a function table is, and how and when to use a function table to represent a function. We will also explore the rules that define a given function table.

### 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. 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. 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.

### 6. Estimating the Slope of Functions

This lesson will review the definition of the slope of a line, and then go on to talk about how to estimate the slope of a linear function. Once we are comfortable with this process, we will look at using tangent lines to estimate the slopes of non-linear functions at a given point.

### 7. Direct and Inverse Variation Problems: Definition & Examples

In this lesson, you'll learn how to approach questions about direct and inverse variation with a simple explanation of what the terms mean and how to apply them to problems.

### 8. Graphing Absolute Value Functions

The purpose of this lesson is to define what is meant by the absolute value of a number and then to extend this idea to define the parent function of absolute value.

### 9. Writing & Graphing Linear Functions

We can show the relationship between two variables using a table, a graph or an equation. In this lesson, you will learn how to write and graph linear functions.

### 10. 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.

### 11. Calculating the Slope of a Line: Point-Slope Form, Slope-Intercept Form & More

Being able to calculate the slope of a line is a very useful skill to have. Why? Watch this video lesson to find out and learn how to find the slope when working with various equations and various lines.

### 12. Standard Form: Equations & Formulas

Standard form is one of many ways to write the equation of a line. In this lesson, you'll learn how to write a line in standard form, and we'll discuss why it's important.

### 13. Residual Plots: Definition & Example

This lesson will look at the definition of a residual, how to make a residual plot, and how to use a residual plot to evaluate the fit of a prediction equation. You will also compare the sum of the squared residuals.

### 14. Problem Solving Using Linear Regression: Steps & Examples

Linear regression can be a powerful tool for predicting and interpreting information. Learn to use two common formulas for linear regression in this lesson.

### 15. Transforming Linear & Absolute Value Functions

In this lesson, we'll find out what happens to the graph of a line when the values of the slope and y-intercept are changed in an equation. We'll also discuss what happens when you change values in the equation of an absolute value function.

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### Other Chapters

Other chapters within the Explorations in Core Math - Algebra 1: Online Textbook Help course

- Explorations in Core Math Algebra 1 Chapter 1: Equations
- Explorations in Core Math Algebra 1 Chapter 2: Inequalities
- Explorations in Core Math Algebra 1 Chapter 3: Functions
- Explorations in Core Math Algebra 1 Chapter 5: Systems of Equations and Inequalities
- Explorations in Core Math Algebra 1 Chapter 6: Exponents and Polynomials
- Explorations in Core Math Algebra 1 Chapter 7: Factoring Polynomials
- Explorations in Core Math Algebra 1 Chapter 8: Quadratic Functions and Equations
- Explorations in Core Math Algebra 1 Chapter 9: Exponential Functions
- Explorations in Core Math Algebra 1 Chapter 10: Data Analysis