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GeorgiaMaths

Linear Equations, Inequalities, and Systems

6 dot points across 6 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you graph a linear equation from any of its forms, and how do you read the slope and intercepts from a graph?

Graph linear equations in two variables and identify key features (slope, x-intercept, y-intercept) from slope-intercept, point-slope, and standard form (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on graphing linear equations in two variables, using slope-intercept form to plot a line, finding x- and y-intercepts from standard form, and reading slope and intercepts from a graph.
9 min answer →

How do you graph a linear inequality in two variables, and how do you find the solution region of a system of inequalities?

Graph linear inequalities in two variables using a boundary line and shading, and find the solution region of a system of linear inequalities (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on graphing linear inequalities in two variables, choosing a solid or dashed boundary line, shading the correct half-plane with a test point, and finding the overlapping solution region of a system of linear inequalities.
10 min answer →

How do you solve a linear equation in one variable, and when does an equation have one solution, no solution, or infinitely many?

Solve linear equations in one variable, including equations with variables on both sides and rational coefficients, and identify equations with one, none, or infinitely many solutions (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on solving linear equations in one variable, clearing fractions, collecting variables on one side, and recognizing when an equation has one solution, no solution (a false statement), or infinitely many solutions (an identity).
9 min answer →

How do you solve a linear inequality in one variable, and why does the inequality sign flip when you multiply or divide by a negative?

Solve linear inequalities in one variable, graph the solution on a number line, and interpret the solution set in context (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on solving linear inequalities in one variable, the rule that the inequality reverses when multiplying or dividing by a negative, graphing solutions with open and closed circles, and interpreting solution sets in real contexts.
9 min answer →

How do you solve a system of two linear equations, and what does it mean when a system has no solution or infinitely many?

Solve systems of two linear equations by graphing, substitution, and elimination, and interpret the solution as the point where the lines meet (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on solving systems of two linear equations by graphing, substitution, and elimination, interpreting the solution as the intersection point, and recognizing parallel lines (no solution) and identical lines (infinitely many).
11 min answer →

How do you write the equation of a line from a slope and a point, from two points, or from a real-world description?

Write linear equations in two variables from a slope and a point, from two points, and from a real-world context, and interpret slope and intercept in the model (A.PAR, Patterning and Algebraic Reasoning).
A Georgia Milestones Algebra: Concepts & Connections answer on writing the equation of a line from a slope and a point, from two points using the slope formula then point-slope form, and from a real-world context, with interpretation of the slope as a rate and the y-intercept as a starting value.
10 min answer →