Algebra 1 Study Guide Flashcards

Linear Equations

• Defined as an equation involving two variables that produces a straight line when graphed.

Slope Intercept

• The format y = mx + b where m represents the slope and b is the y-intercept.
• Example: In y = 4x + 3, the slope is 4 and the y-intercept is 3.

Point-Slope Form

• Expressed as y - y₁ = m(x - x₁), focusing on the slope of the line and a known point on the line.

Parallel and Perpendicular Lines

• Parallel lines do not intersect in a plane.
• Perpendicular lines intersect at a 90° angle.

Graphing Linear Equations in Slope-Intercept Form

• Start by identifying the y-intercept and plotting the point.
• Use the slope to find a second point, then draw the line connecting the two points.

Graphing Using Intercepts

• Involves writing a linear equation in standard form to identify intercepts for graphing.

Solving Systems of Equations

• Use substitution by replacing one variable with its equivalent from another equation.
• Example solution: (1, 6) can be obtained via this method.

Solving by Substitution

• First, rearrange one equation to isolate a variable.
• Substitute the found value into another equation to solve for the remaining variable.

Solving by Elimination

• Create equations with matching coefficients for a variable to eliminate it.
• Solve for the remaining variable, then substitute back to find the other variable.

Exponents

• Represents the power to which a base number or expression is raised, usually shown as a superscript.

Product to Power Rule

• Simplifying involving multiplications with exponents by adding the exponents of like bases.

Quotient to Power Rule

• When dividing terms with the same base, subtract the exponents of the base.

Power to Power

• The dimension of power relates to energy over time, with the standard unit being Watts.

Negative Exponents

• A negative exponent indicates reciprocal; move the base to the opposite side of the fraction line and change the exponent to positive.

Zero Exponent Rule

• Any base raised to the power of zero equals one.

Polynomials

• Defined as expressions with more than two algebraic terms, comprising variables raised to various powers.

Multiplying Polynomials

• Multiply coefficients, and add exponents of like bases; after distribution, combine like terms.

Factoring Polynomials

• Involves identifying and extracting common factors from polynomial expressions.

Sequences

• A structured order of related events or items following one another.

Arithmetic Sequences

• A sequence where the difference between consecutive terms remains constant.
• Example: 5, 7, 9, 11, 13, ... presents a common difference of 2.

Explore key concepts from Algebra 1 with these helpful flashcards. Learn about linear equations, slope intercept form, and point-slope form. Perfect for quick study sessions and reviewing important algebraic principles.