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TexasMaths

Writing and Solving Linear Functions, Equations, and Inequalities

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 determine the domain and range of a linear function, including reasonable continuous or discrete values for a real-world situation?

Determine the domain and range of a linear function in mathematical problems, and reasonable domain and range values (continuous and discrete) for real-world situations, representing them using inequalities (TEKS A.2A).
A STAAR Algebra I answer on the domain and range of linear functions (TEKS A.2A), continuous versus discrete situations, reasonable real-world values, and representing domain and range with inequalities.
9 min answer →

How do you write a system of two linear equations from a real-world situation and interpret the solution in context?

Write systems of two linear equations given a table, a graph, a verbal description, or a real-world problem, then solve and interpret the solution in context (TEKS A.2H, A.2I).
A STAAR Algebra I answer on writing and modeling with systems of two linear equations from real-world situations (TEKS A.2H, A.2I), defining variables, building one equation per condition, and interpreting the solution.
10 min answer →

How do you solve a linear equation in one variable, including ones needing the distributive property and variables on both sides?

Solve linear equations in one variable, including those requiring the distributive property and those with variables on both sides, and identify equations with one solution, no solution, or infinitely many (TEKS A.5A).
A STAAR Algebra I answer on solving one-variable linear equations (TEKS A.5A), the inverse-operations routine, the distributive property, variables on both sides, and recognizing one solution, no solution, or infinitely many.
10 min answer →

How do you solve a linear inequality in one variable, when do you flip the sign, and how do you graph and interpret the solution?

Solve linear inequalities in one variable, including those requiring the distributive property and those with variables on both sides, graph the solution, and interpret it in context (TEKS A.5B).
A STAAR Algebra I answer on solving one-variable linear inequalities (TEKS A.5B), the rule for flipping the sign when multiplying or dividing by a negative, graphing on a number line, and interpreting in context.
9 min answer →

How do you solve a system of two linear equations by graphing, substitution, and elimination, and tell how many solutions it has?

Solve systems of two linear equations in two variables by graphing, substitution, and elimination, and determine whether a system has one solution, no solution, or infinitely many (TEKS A.5C, A.3E).
A STAAR Algebra I answer on solving systems of two linear equations by graphing, substitution, and elimination (TEKS A.5C, A.3E), and identifying one solution, no solution (parallel), or infinitely many (same line).
10 min answer →

How do you write a linear function or equation to model a real-world situation, and evaluate it using function notation?

Write linear functions that model the relationship between two quantities from a description, table, or graph, write an equation representing a functional relationship, and evaluate functions in function notation (TEKS A.2C, A.2G, A.12B).
A STAAR Algebra I answer on writing linear functions to model situations, identifying initial value and rate, function notation f(x), and evaluating functions (TEKS A.2C, A.2G, A.12B).
10 min answer →