Front
Slope-Intercept Form
Back
y = mx + b
m is slope, b is y-intercept. Example: y = 2x + 3.
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College Algebra - 40 Essential Topics
Master algebra with 40 flashcards covering linear, quadratic, polynomial, and exponential equations with examples.
AnyFlashcards40 cards
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Front
Power Property of Logs
Back
log_b(M^p) = p · log_b(M)
Example: log(x³) = 3 log(x).
Front
Change of Base Formula
Back
log_b(a) = log(a) / log(b)
Allows calculation of logs with any base using common logs. Example: log₂(5) = log(5)/log(2).
Front
Natural Logarithm (ln)
Back
A logarithm with base e (approx. 2.718)
ln(x) is the same as log_e(x). Example: ln(e) = 1.
Front
Inverse Property of Logs/Exponents
Back
b^(log_b(x)) = x and log_b(b^x) = x
Logs and exponentials 'undo' each other. Example: e^(ln(5)) = 5.
Front
Point-Slope Form
Back
y - y₁ = m(x - x₁)
Used when given a point (x₁, y₁) and slope m. Example: y - 2 = 3(x - 1).
Front
Standard Form of a Linear Equation
Back
Ax + By = C
A, B, and C are integers; A is usually positive. Example: 2x + 3y = 6.
Front
Slope Formula (Two Points)
Back
m = (y₂ - y₁) / (x₂ - x₁)
Calculates the 'rise over run' between two points. Example: (1,2) and (3,6) → m = 2.
Front
Slopes of Parallel Lines
Back
m₁ = m₂
Parallel lines have the exact same slope. Example: y = 5x + 1 and y = 5x - 4.
Front
Slopes of Perpendicular Lines
Back
m₁ = -1 / m₂
Slopes are negative reciprocals (product is -1). Example: 2/3 and -3/2.
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