Algebra Unit Review: Key Formulas & Concepts
A cumulative review of coordinate graphing, linear equations, systems, exponents, polynomials, and factoring.
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Questions Covered in This Set
10 cards to master
What is the slope formula between two points?
m = (y₂ − y₁)/(x₂ − x₁), the rise over the run — the rate of change.
Name the three forms of a linear equation.
Slope-intercept: y = mx + b; Point-slope: y − y₁ = m(x − x₁); Standard: Ax + By = C.
In a real-world model, what becomes the slope and what becomes the intercept?
Every 'per' rate (e.g., $15 per month) is the slope; every flat fee or starting amount (e.g., $30 to join) is the y-intercept.
What do the three possible outcomes of a system of two linear equations look like?
One intersection = one solution; parallel lines = no solution; the same line = infinitely many solutions.
List the main exponent rules.
xᵃ·xᵇ = xᵃ⁺ᵇ; xᵃ/xᵇ = xᵃ⁻ᵇ; (xᵃ)ᵇ = xᵃᵇ; x⁰ = 1; x⁻ⁿ = 1/xⁿ.
What is the zero-product property and how does it solve quadratics?
If a·b = 0 then a = 0 or b = 0. So x² − 2x − 15 = (x+3)(x−5) = 0 gives x = −3 or x = 5.
State the quadratic formula.
x = [−b ± √(b² − 4ac)] / (2a) — it works even when factoring fails.
Find the equation of the line through (2, 7) and (5, 1).
m = (1−7)/(5−2) = −2; point-slope gives y − 7 = −2(x − 2), so y = −2x + 11.
Solve the system 3x + 2y = 16 and x − 2y = 0 by elimination.
Add the equations: 4x = 16, x = 4; then 4 − 2y = 0 so y = 2. Solution (4, 2).
What should you always do FIRST when factoring?
Pull out the greatest common factor. Example: 2x² + 10x = 2x(x + 5) = 0, so x = 0 or x = −5.
