A1.LFE

Linear Functions, Equations, & Inequalities

A1.LFE.1Represent and solve real-world problems, using linear expressions, equations, and inequalities in one variable.A1.LFE.10Translate among equivalent forms of equations for linear functions, including standard, point-slope, and slope-intercept forms; recognize that each form reveals key features in a given context.A1.LFE.11Solve systems of linear equations by substitution, elimination, and graphing with and without a real-world context; understand that the solutions will be the same regardless of the method for solving.A1.LFE.12Solve a system of equations consisting of a linear equation and a quadratic equation in two variables graphically with the assistance of technology.A1.LFE.13Explain why a solution to the equation 𝑓(𝑥)=𝑔(𝑥) is the x-coordinate where the y-coordinate of 𝑓(𝑥) and 𝑔(𝑥) are the same using graphs, tables, or approximations. Include cases where 𝑓(x) and/or 𝑔(𝑥) are linear, quadratic, absolute value, and exponential.A1.LFE.14Solve linear inequalities and systems of linear inequalities in two variables by graphing.A1.LFE.15Write linear equations that model the relationship between two quantities and produce a graph of the equation.A1.LFE.16Graph linear functions expressed as an equation and show intercepts of the graph without technology.A1.LFE.17Graph absolute value functions expressed as an equation with and without technology, showing intercepts and end behavior.A1.LFE.18Graph and generalize the effect of transformations on linear and absolute value functions. Transformations include: stretches, compressions, vertical, and horizontalA1.LFE.19Given the graph of a linear function, explain the effects of the transformation from the parent function, 𝑦=𝑥.A1.LFE.2Construct linear functions from arithmetic sequences with and without context.A1.LFE.20Write linear functions that provide a reasonable fit to data and use them to make predictions, with and without technology; interpret the slope and y-intercept in context.A1.LFE.21Calculate, using technology, the correlation coefficient between two quantitative variables and interpret this quantity as a measure of the strength of the linear association.A1.LFE.22Compare and contrast correlation and causation in real-world problems.A1.LFE.3Solve linear formulas for a specified variable.A1.LFE.4Solve linear equations, linear inequalities, and absolute value equations in one variable, including those with rational number coefficients, and variables on both sides of the equal or inequality sign; solve them fluently, explaining the process used.A1.LFE.5Determine the domain and range of linear functions in mathematical problems.A1.LFE.6Determine reasonable domain and range values of linear functions representing real-world situations, both continuous and discrete; interpret the solution as reasonable or unreasonable in context.A1.LFE.7Interpret the key features of a linear and absolute value functions that models a relationship between two quantities in a given context.A1.LFE.8Flexibly use different representations of a linear function, including graphs, tables, and equations.A1.LFE.9Calculate and interpret the rate of change of a linear function represented in a table, graph, or as an equation in context of real-world and mathematical problems.
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