# Ch 8: ISTEP+ Grade 7 Math: Linear Equations

### About This Chapter

## ISTEP+ Grade 7 Math: Linear Equations - Chapter Summary

You can access this chapter to ensure your students understand linear equations before they take the ISTEP+ Grade 7 Math exam. Our expert instructors designed these lessons to review:

- The definition of a linear equation and how to write one
- Intercepts, standard form and graphing
- Linear equations in abstract algebra
- Factoring and equivalent linear expressions
- Systems of equations
- Steps for solving systems of linear equations
- How to solve equations of the form px + q =r and p(x + q) = r

The interactive quizzes and chapter test will give students the chance to find solutions to problems that involve linear equations. If they need further practice, the quizzes link back to the video lessons to encourage review.

### 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. What is Factoring in Algebra? - Definition & Example

Factoring with ordinary numbers involves knowing that 6 is the product of 2 and 3. But what about factoring in algebra? In this lesson, we'll learn the essential elements of algebra factoring.

### 7. Equivalent Linear Expressions

We use algebraic expressions to represent real world phenomena all the time. In this lesson, we will look at equivalent linear expressions and explore how to identify and create these types of expressions.

### 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. How to Solve a System of Linear Equations in Two Variables

Watch this video lesson to learn how you can solve a system of linear equations in two variables by using the substitution method. Learn how easy it is to use on any linear system in two variables.

### 11. How to Solve a Linear System in Three Variables With a Solution

After watching this video lesson, you will be able to solve a linear system in three variables using the elimination method. Learn the simple operations that are needed to solve your system.

### 12. How to Solve a Linear System in Three Variables With No or Infinite Solutions

In this video lesson, you will learn to recognize when a linear system has no solution or an infinite number of solutions. You will also learn how to go about solving each of these types of systems.

### 13. Equations in the Form px + q = r and p(x + q) = r

After reading this lesson, you'll learn how to solve algebraic problems such as px + q = r and p(x + q) = r easily. You'll also see what kinds of real world problems are represented by these equations.

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### Other Chapters

Other chapters within the ISTEP+ Grade 7 - Math: Test Prep & Practice course

- ISTEP+ Grade 7 Math: Prime Factorization
- ISTEP+ Grade 7 Math: Square Roots
- ISTEP+ Grade 7 Math: Rational & Irrational Numbers
- ISTEP+ Grade 7 Math: Operations with Rational Numbers
- ISTEP+ Grade 7 Math: Math Properties
- ISTEP+ Grade 7 Math: Algebraic Expressions
- ISTEP+ Grade 7 Math: Graphing Basics
- ISTEP+ Grade 7 Math: Inequalities
- ISTEP+ Grade 7 Math: Slope & Rate of Change
- ISTEP+ Grade 7 Math: Ratios & Proportions
- ISTEP+ Grade 7 Math: Lines & Angles
- ISTEP+ Grade 7 Math: Geometric Constructions
- ISTEP+ Grade 7 Math: Triangles
- ISTEP+ Grade 7 Math: Similar Figures
- ISTEP+ Grade 7 Math: Area & Circumference
- ISTEP+ Grade 7 Math: Complex Figures
- ISTEP+ Grade 7 Math: Populations & Statistics
- ISTEP+ Grade 7 Math: Data Analysis & Statistics
- ISTEP+ Grade 7 Math: Probability
- ISTEP+ Grade 7 Math: Mathematical Process
- ISTEP+ Grade 7 - Math Flashcards