Questions and Answers
What is the relationship in direct variation?
What does the average rate of change represent?
Slope
The formula for inverses of linear functions involves ______.
switching x and y
What is a piece-wise linear function?
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How do you solve the equation |-2x + 7| = 25?
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What does the elimination and substitution method refer to?
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What does 'No Solutions' represent in set notation?
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What does linear modeling refer to in the context of equations?
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What is linear regression?
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Study Notes
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.
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Description
This quiz features flashcards designed to help reinforce key concepts in Algebra 2, focusing on unit 2 topics. Learn about direct variation, average rate of change, and different forms of linear equations. Perfect for students preparing for exams or needing a quick review of these essential algebra concepts.
