Unit 2
Reasoning with Linear Equations & Inequalities
Georgia virtual school learning modules

VOCABULARY Flash Cards

Unit 2 Study Guide  
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IN THIS UNIT, STUDENTS WILL BE ABLE TO:
 Solve and justify the solution of linear equations in one variable.
 Rearrange formulas to highlight a quantity of interest, using the same reasoning as solving equations.
 Solve and justify the solution of linear inequalities in one variable.
 Create linear equations and inequalities in one variable and use them in a contextual situation to solve problems.
 Create equations in two or more variables to represent relationships between quantities.
 Graph equations in two variables on a coordinate plane and label the axes and scales.
 Graph linear functions f(x) = x and understand pointslope form as yy1 = m(xx1), slopeintercept form as f(x) = mx + b, and
standard form as Ax + By = C. Then determine the x and yintercepts for each graph.
 Solve systems of linear equations in two variables exactly and approximately.
 Show and explain why the elimination method works.
 Write and use a system of equations to solve real world problems.
 Graph inequalities in two variables on a coordinate plane and label the axes and scales.
 Write and use a system of inequalities to solve real world problems.
 Explain the difference and relationship between domain and range and find the domain and range of a function from a function
equation, table or graph.
 Understand function notation and recognize how the input of a function, x, corresponds to its output, f.
 Graph a function that algebraically models a relationship between two quantities and interpret the graphs’ key characteristics:
 x and y intercepts  ordered pairs  increasing intervals
 decreasing intervals  positive intervals  negative intervals
 symmetries  positive end behavior  negative end behavior
 Calculate and interpret the average rate of change of a function presented symbolically or in a table over a specified interval.
 Estimate the rate of change from a graph.
 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by
verbal descriptions).
 Determine any element of a sequence by inputting its position into a given formula.
 Distinguish between a recursive and explicit formula, and know what each will reveal about a given sequence.
 Write explicit and recursive formulas for arithmetic sequences, and translate between the recursive and explicit forms of arithmetic
sequences.
 Solve and justify the solution of linear equations in one variable.
 Rearrange formulas to highlight a quantity of interest, using the same reasoning as solving equations.
 Solve and justify the solution of linear inequalities in one variable.
 Create linear equations and inequalities in one variable and use them in a contextual situation to solve problems.
 Create equations in two or more variables to represent relationships between quantities.
 Graph equations in two variables on a coordinate plane and label the axes and scales.
 Graph linear functions f(x) = x and understand pointslope form as yy1 = m(xx1), slopeintercept form as f(x) = mx + b, and
standard form as Ax + By = C. Then determine the x and yintercepts for each graph.
 Solve systems of linear equations in two variables exactly and approximately.
 Show and explain why the elimination method works.
 Write and use a system of equations to solve real world problems.
 Graph inequalities in two variables on a coordinate plane and label the axes and scales.
 Write and use a system of inequalities to solve real world problems.
 Explain the difference and relationship between domain and range and find the domain and range of a function from a function
equation, table or graph.
 Understand function notation and recognize how the input of a function, x, corresponds to its output, f.
 Graph a function that algebraically models a relationship between two quantities and interpret the graphs’ key characteristics:
 x and y intercepts  ordered pairs  increasing intervals
 decreasing intervals  positive intervals  negative intervals
 symmetries  positive end behavior  negative end behavior
 Calculate and interpret the average rate of change of a function presented symbolically or in a table over a specified interval.
 Estimate the rate of change from a graph.
 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by
verbal descriptions).
 Determine any element of a sequence by inputting its position into a given formula.
 Distinguish between a recursive and explicit formula, and know what each will reveal about a given sequence.
 Write explicit and recursive formulas for arithmetic sequences, and translate between the recursive and explicit forms of arithmetic
sequences.