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Questions and Answers
What is the relationship in direct variation?
What is the relationship in direct variation?
What does the average rate of change represent?
What does the average rate of change represent?
Slope
The formula for inverses of linear functions involves ______.
The formula for inverses of linear functions involves ______.
switching x and y
What is a piece-wise linear function?
What is a piece-wise linear function?
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How do you solve the equation |-2x + 7| = 25?
How do you solve the equation |-2x + 7| = 25?
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What does the elimination and substitution method refer to?
What does the elimination and substitution method refer to?
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What does 'No Solutions' represent in set notation?
What does 'No Solutions' represent in set notation?
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What does linear modeling refer to in the context of equations?
What does linear modeling refer to in the context of equations?
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What is linear regression?
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.
