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Mathematics | Grade : 8
Domain - Expressions and Equations
Cluster - Analyze and solve linear equations and pairs of simultaneous linear equations.
[8.EE.C.8.a] - 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.
- Linear equation
Any equation that can be written in the form Ax + By + C = 0 where A and B cannot both be 0. The graph of such an equation is a line. - Variable
A quantity that can change or that may take on different values. Refers to the letter or symbol representing such a quantity in an expression, equation, inequality, or matrix.
[AI.A-CED.A.2] -
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
[AI.A-CED.A.3] -
Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
[AI.A-CED.A.4] -
Rearrange formulas to highlight a quantity of interest using the same reasoning as in solving equations (Properties of equality).* For example, rearrange Ohm’s law R=V2/P to solve for voltage, V. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt.
[AI.A-REI.C.6] -
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
[AI.A-REI.C.7] -
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.
[AI.A-REI.D.10] -
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation.
[AI.A-REI.D.12] -
Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
[GEO.G-GPE.B.5] -
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
[MI.A-CED.A.2] -
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.*
[MI.A-CED.A.3] -
Represent constraints by linear equations or inequalities, and by systems of linear equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.* For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
[MI.A-CED.A.4] -
Rearrange formulas to highlight a quantity of interest, using the same reasoning (Properties of equality) as in solving equations.* For example, rearrange Ohm’s law, V = IR, to solve for resistance, R. Manipulate variables in formulas used in financial contexts such as for simple interest, I=Prt .
[MI.A-REI.C.6] -
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
[MI.A-REI.D.10] -
Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Show that any point on the graph of an equation in two variables is a solution to the equation.
[MI.A-REI.D.12] -
Graph the solutions of a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set of a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
[MI.G-GPE.B.5] -
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
[MII.A-REI.C.7] -
Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically. For example, find the points of intersection between the line y = –3x and the circle x2 + y2 = 3.