Algebra 1 — Essential Formulas (Quick Reference)

A printable, exam-day reference for every formula and pattern that shows up on the Texas Algebra 1 Credit by Exam. Use it for last-minute review and as a check-list during practice.

Linear Equations

• Slope-intercept form: y = mx + b — m is slope, b is the y-intercept
• Point-slope form: y − y₁ = m(x − x₁)
• Standard form: Ax + By = C
• Slope from two points: m = (y₂ − y₁) / (x₂ − x₁)
• Parallel lines: same slope, different intercept
• Perpendicular lines: slopes multiply to −1

Solving Equations

• One-variable linear: isolate the variable using inverse operations
• Linear inequality: same as equations, but flip the sign when multiplying or dividing by a negative
• Absolute value: |x| = k → x = k or x = −k

Systems of Linear Equations

• Substitution: solve one equation for a variable, substitute into the other
• Elimination: add or subtract to cancel a variable
• One solution: different slopes
• No solution: same slope, different y-intercept (parallel)
• Infinite solutions: same line (proportional equations)

Exponent Rules

• x^a · x^b = x^a+b
• x^a / x^b = x^a−b
• (x^a)^b = x^ab
• x⁰ = 1 (for x ≠ 0)
• x^−a = 1 / x^a
• x^1/n = ⁿ√x

Polynomials

• FOIL: (a + b)(c + d) = ac + ad + bc + bd
• Difference of squares: a² − b² = (a + b)(a − b)
• Perfect square trinomial: a² ± 2ab + b² = (a ± b)²

Quadratics

• Standard form: ax² + bx + c = 0
• Factor & zero product: if (x − p)(x − q) = 0 then x = p or x = q
• Quadratic formula: x = (−b ± √(b² − 4ac)) / (2a)
• Discriminant: b² − 4ac → positive = 2 real, zero = 1 real, negative = 0 real solutions

Word-Problem Setups

• Rate problem: distance = rate × time → d = rt
• Mixture/cost: total = price × quantity, summed across components
• Percent change: (new − old) / old × 100%

Common Test Mistakes

• Forgetting to flip the inequality sign when multiplying by a negative
• Mixing up slope formula rise/run order — always (y₂ − y₁) on top
• Distributing negatives wrong: −(a − b) = −a + b, not −a − b
• Using only one root from a quadratic (always check both)

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