# Ch 15: Graphing Linear Equations & Inequalities: Help and Review

### About This Chapter

## Who's it for?

Anyone who needs help learning or mastering SAT mathematics level 2 material will benefit from taking this course. There is no faster or easier way to prepare for this SAT math subject test. Among those who would benefit are:

- Students who have fallen behind in understanding how to graph linear equations and inequalities or absolute value equations
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about linear equations and inequalities for the SAT
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources

## How it works:

- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Graphing Linear Equations & Inequalities chapter exam.

## Why it works:

**Study Efficiently**: Skip what you know, review what you don't.**Retain What You Learn**: Engaging animations and real-life examples make topics easy to grasp.**Be Ready on Test Day**: Use the Graphing Linear Equations & Inequalities chapter exam to be prepared.**Get Extra Support**: Ask our subject-matter experts any linear equations and inequalities question. They're here to help!**Study With Flexibility**: Watch videos on any web-ready device.

## Students will review:

This chapter helps students review the concepts in a linear equations and inequalities unit of a standard math course. Topics covered include:

- Writing the standard form of a linear equation
- Finding the slope and intercepts of a line
- Graphing undefined and zero slope
- Graphing 1- and 2-variable inequalities
- Using the point-slope formula
- Graphing absolute value equations
- Performing dilations and reflections
- Using the distance and midpoint formulas

### 1. Identify Where a Function is Linear, Increasing or Decreasing, Positive or Negative

Functions can appear in the form of opposites, which is one way of identifying what type they are. Discover how a function can be linear or nonlinear, increasing or decreasing, and positive or negative.

### 2. Linear Equations: Intercepts, Standard Form and Graphing

To solve a linear equation, begin by determining whether it is written in the standard form or the slope-intercept form. Explore the differences between the slope-intercept form and the standard form of a linear equation, and learn how to graph the point of intercept for each.

### 3. How to Find and Apply The Slope of a Line

The slope of a line refers to how steep it is whether it is positive or negative. Study the definition and types of slopes, learn how to find and apply the slope of a line, and practice using points and equations.

### 4. How to Find and Apply the Intercepts of a Line

The intercepts of a line can be calculated through the x-intercept and the y-intercept. Learn about intercepts and the definition of x- and y-intercepts, and apply that learning through practice problems.

### 5. Graphing Undefined Slope, Zero Slope and More

When the variable determining the slope is mathematically impossible but can still be graphed, it is referred to as an undefined slope. Learn how to compute formulas to graphs that have either undefined slope or zero slopes, and discover what this means for the line.

### 6. How to Graph 1- and 2-Variable Inequalities

The number of variable inequalities in an equation affects how it is solved and graphed. Learn more about the properties of one-variable and two-variable inequalities and how to graph them on number lines and coordinate planes.

### 7. Graphing Inequalities: Practice Problems

Whether an inequality has one or two variables is an important distinction when graphing these types of algebraic expressions. Learn more about when to use a number line or a coordinate plane when graphing inequalities by solving some practice problems.

### 8. Equation of a Line Using Point-Slope Formula

The point-slope formula is composed of a specific point of coordinates and a slope indicating a type of change over a given variable, such as distance over time. Identify the use of point-slope formula in graphing a line through provided examples.

### 9. How to Graph an Absolute Value and Do Transformations

Absolute value graphs are translations of standard graphs, created by using linear representations in the shape of a 'V' rather than the standard axis intersect. In this lesson, learn two of the most common transformations observed on absolute value graphs.

### 10. Graphing Absolute Value Equations: Dilations & Reflections

An absolute value is the numerical distance from zero and can be used in equations and graphed as dilations or reflections. Discover how translations apply to absolute value equations, and how dilations and reflections differ and are graphed.

### 11. How to Use The Distance Formula

The distance formula is a shortened form of the Pythagorean Theorem. Learn about the Pythagorean Theorem and the distance formula, along with examples of how the formula is used.

### 12. How to Use The Midpoint Formula

The midpoint formula enables us to find the midpoint of a line segment when we know the endpoints. Learn about line segments, midpoints, and how to use the midpoint formula. Explore examples, and understand that the midpoint can be found on both vertical and horizontal line segments.

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### Other Chapters

Other chapters within the SAT Mathematics Level 2: Help and Review course

- Basic Math Review: Help and Review
- Square Roots: Help and Review
- Basic Algebraic Expressions in Math: Help and Review
- Exponents in Math: Help and Review
- Linear Equations & Inequalities in Algebra: Help and Review
- Absolute Value Equations & Inequalities: Help and Review
- Polynomials in Algebra: Help and Review
- Functions in Math: Help and Review
- Rational Expressions in Algebra: Help and Review
- Matrices: Help and Review
- Sequences and Series in Math: Help and Review
- Exponentials and Logarithms in Math: Help and Review
- Complex Numbers in Math: Help and Review
- Coordinate Geometry Basics: Help and Review
- Advanced Coordinate Geometry: Help and Review
- Three-Dimensional Geometry: Help and Review
- Overview of Trigonometry: Help and Review
- Probability, Combinations & Permutations: Help and Review
- Working with Data & Statistics: Help and Review
- Logic: Help and Review
- Limits in Math: Help and Review