Linear Equations
A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and the first power of a variable. The general form of a linear equation in one variable is:
ax + b = 0
Where a and b are constants, and x is the variable. Linear equations can also be written in the form y = mx + b, where m is the slope and b is the y-intercept. In this form, the equation represents a straight line on a graph.
Solving Linear Equations
To solve a linear equation, you can use several methods, such as:
- Substitution: Substitute one expression from the equation into the other, and solve for the variable.
- Elimination: Add or subtract the equations to eliminate one variable, and then solve for the remaining variable.
- Graphing: Plot the equations on a graph and find the point of intersection.
Study Guide
When studying linear equations, it's important to understand the following key concepts:
- Slope-Intercept Form: Understand how to represent a linear equation in the form y = mx + b, where m is the slope and b is the y-intercept.
- Graphing: Practice graphing linear equations on the coordinate plane and understanding the relationship between the equation and its graphical representation.
- Solving Equations: Learn and practice different methods for solving linear equations, including substitution, elimination, and graphing.
- Applications: Understand real-world applications of linear equations, such as calculating costs, determining rates of change, and predicting trends.
By mastering these concepts and practicing solving various linear equations, you can develop a strong understanding of this fundamental algebraic topic.
[Linear Equations] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Sixth Grade. Algebraic Equations
Study Guide
Algebraic Equations 
Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations Worksheet/Answer key
Algebraic Equations
Worksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Algebra (NCTM)
Represent and analyze mathematical situations and structures using algebraic symbols.
Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations
Grade 6 Curriculum Focal Points (NCTM)
Algebra: Writing, interpreting, and using mathematical expressions and equations
Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.