Linear Equations
Unit description: Students will extend their understanding of equations to represent real world contexts to consider linear equations. Students will leave this unit able to solve linear equations and recognize the number of solutions to a linear equation.
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Essential Outcomes of the Unit
Expressions and Equations
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways.
Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.7b Solve linear equations with rational number coefficients, including equations whose solutions require expanding expressions using the distributive property and combining like terms. Note: This includes equations that contain variables on both sides of the equation.
Other Standards Addressed in the Unit
Expressions and Equations
Understand the connections between proportional relationships, lines, and linear equations.
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
Analyze and solve linear equations and pairs of simultaneous linear equations.
8.EE.7 Solve linear equations in one variable.
8.EE.7a Recognize when linear equations in one variable have one solution, infinitely many solutions, or no solutions. Give examples and show which of these possibilities is the case by successively transforming the given equation into simpler forms
8.EE.8 . Analyze and solve pairs of simultaneous linear equations.
8.EE.8a Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. Recognize when the system has one solution, no solution, or infinitely many solutions
8.EE.8b Solve systems of two linear equations in two variables with integer coefficients: graphically, numerically using a table, and algebraically. Solve simple cases by inspection.
8.EE.8c Solve real-world and mathematical problems involving systems of two linear equations in two variables with integer coefficients
Essential Questions and Big Ideas
What is a linear equation in one variable?
- A linear equation in one variable, is one where there is only one variable and that variable does not have an exponent.
How do I simplify terms in an equation?
- Like terms can be combined or subtracted.
- Like terms are terms with the same variable.
- The distributive property can be used to expand an expression or equation.
How can I determine the number of solutions to a linear equation?
- If an equation ends with an untrue statement, there are no solutions.
- If an equation ends with a true statement, there are infinite solutions.
- If an equation ends with an x = statement, there is one solution.
Download the complete Linear Equations framework to customize for your own planning.