Algebra 2 Unit 2 Review Flashcards

Direct Variation

• Relationship between variables x and y represented by the equation y = kx.
• Equivalent expression: y/x = k, where k is the constant of variation.

Average Rate of Change

• This is synonymous with slope in the context of linear functions.

Slope-Intercept Form of a Line

• A linear equation expressed as y = mx + b.
• m denotes the slope and b represents the y-intercept.

Point-Slope Form of a Line

• This form is expressed as y - y₁ = m(x - x₁).
• It is useful for writing equations of lines when a point and slope are known.

Inverses of Linear Functions

• Inverses are found by switching x and y in the original function.
• Graphically represented by reflection over the line y = x.
• Notation is y = f⁻¹(x).

Piece-wise Linear Function

• Defined by multiple linear functions, each valid over specific intervals of the domain.

How to Solve: |-2x + 7| = 25

• To solve absolute value equations, set up two scenarios:
  • -2x + 7 = 25
  • -2x + 7 = -25

Absolute Value Function

• A function that returns the non-negative value of its argument.

Elimination and Substitution Method

• Two strategies for solving systems of linear equations.
• Elimination involves adding or subtracting equations to eliminate a variable.
• Substitution involves solving one equation for a variable and substituting it into another.

Solution to System of Equations

• The solution set { x = 7, y = 3, z = -2 } satisfies the equations:
  • 2x + y + z = 15
  • 6x - 3y - z = 35
  • -4x + 4y - z = -14

No Solutions

• Indicated by the symbol ∅ or the empty set { }.
• Occurs when equations contradict each other, meaning no common solution exists.

Linear Modeling

• Translating real-world situations into linear equations.
• Key terms: "rate" refers to slope; "initial" denotes y-intercept.

Linear Regression

• The process of fitting a line of best fit to data points to describe relationships.

Performing a Linear Regression on the TI-Nspire

• Specific instructions or methods are used to execute linear regression calculations on the TI-Nspire calculator.