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Linear 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 translate a real-world situation into an equation or inequality you can solve?

Create equations and inequalities in one variable from a context and use them to solve problems (LA A1: A-CED.A.1).
A Louisiana LEAP 2025 Algebra I answer on creating equations and inequalities (LA A1: A-CED.A.1): defining a variable, translating words into symbols, choosing the right comparison sign, and solving and interpreting the result.
10 min answer →

What do slope and the intercepts tell you about a line, and how do you find them from an equation, a graph, or a table?

Find the slope and intercepts of a linear function and interpret them in context, working from an equation, a graph, or a table (LA A1: A-REI.D, F-IF.B).
A Louisiana LEAP 2025 Algebra I answer on slope and intercepts (LA A1: A-REI.D, F-IF.B): the slope formula, slope-intercept form, finding intercepts, and interpreting slope as a rate of change.
10 min answer →

How do you rearrange a formula to solve for a different variable, treating the other letters as constants?

Rearrange formulas and literal equations to highlight a quantity of interest, using the same reasoning as solving equations (LA A1: A-CED.A.4).
A Louisiana LEAP 2025 Algebra I answer on literal equations (LA A1: A-CED.A.4): solving a formula for a chosen variable, treating other letters as constants, and undoing operations in reverse order.
9 min answer →

How do you solve a linear equation in one variable, and how does each step follow from the properties of equality?

Solve linear equations in one variable, including equations with variables on both sides and with letter coefficients, and recognize when an equation has one solution, no solution, or infinitely many (LA A1: A-REI.B.3).
A Louisiana LEAP 2025 Algebra I answer on solving linear equations (LA A1: A-REI.B.3): the properties of equality, clearing fractions and parentheses, variables on both sides, and recognizing no-solution and identity cases.
10 min answer →

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

Solve linear inequalities in one variable and graph the solution set on a number line, reversing the inequality when multiplying or dividing by a negative (LA A1: A-REI.B.3).
A Louisiana LEAP 2025 Algebra I answer on solving linear inequalities (LA A1: A-REI.B.3): the same steps as equations, flipping the sign for a negative multiply or divide, and graphing the solution on a number line.
9 min answer →

How do you write the equation of a line from a slope and a point, two points, or a graph?

Write the equation of a line in slope-intercept and point-slope form given a slope and a point, two points, or a graph (LA A1: F-IF, A-CED, building linear models).
A Louisiana LEAP 2025 Algebra I answer on writing linear equations: using point-slope and slope-intercept form, finding the equation from two points, and from a slope and a point.
9 min answer →