Heart of Algebra Summary

SAT Math · Axiom Academy

Complete recap of all major concepts and test-day tips Congratulations on completing Unit 2! You now understand: The slope tells you how much y changes for every 1 unit change in x. In context, this is often a rate (cost per month, miles per hour, etc.) The y-intercept is where the line crosses the y-axis (when x = 0). In context, this is often initial cost, initial population, starting distance, etc. One solution (intersect), no solution (parallel), or infinite solutions (same line). When solving, 0 = 0 means infinite; 0 = (non-zero) means none. |x| means distance from x to 0. |x - 3| means distance from x to 3. This intuition helps solve equations and inequalities. When you multiply or divide both sides of an inequality by a negative number, flip the >, <, ≥, or ≤ sign. This is a common error. . It's 2x + 6 . Always multiply everything inside. -2x > 10 divides to x -5 . Flip when multiplying/dividing by negative! |x| = 5 has TWO solutions: x = 5 and x = -5 . Don't forget the negative one. "At least 10" is ≥, "less than 5" is <, "at most 20" is ≤. Get these right! Parallel: same slope. Perpendicular: slopes multiply to -1. Know the difference! Always plug your solution back into the original equation. It only takes 10 seconds and catches careless mistakes. Memorize the key formulas: slope formula, line forms, inequality flip rule Practice solving systems both ways (substitution and elimination) Get comfortable interpreting word problems into equations

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