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Questions and Answers
What does the equation $y=mx+b$ represent?
What does the equation $y=mx+b$ represent?
What is the formula for Slope?
What is the formula for Slope?
Rise over Run
What is the formula for the nth term of an Arithmetic Sequence?
What is the formula for the nth term of an Arithmetic Sequence?
An=A₁+(n-1)d
What is the Point-Slope form of an equation?
What is the Point-Slope form of an equation?
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A function cannot have an arrow that splits.
A function cannot have an arrow that splits.
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What is the characteristic of a Linear Function?
What is the characteristic of a Linear Function?
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What type of line is represented by the equation $x=3$?
What type of line is represented by the equation $x=3$?
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What does the equation $y=2$ represent?
What does the equation $y=2$ represent?
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Match the following terms with their definitions:
Match the following terms with their definitions:
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What is the purpose of a Line of Fit?
What is the purpose of a Line of Fit?
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What is the equation for Direct Variation?
What is the equation for Direct Variation?
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How can you determine a Direct Variation?
How can you determine a Direct Variation?
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What is a system of equations?
What is a system of equations?
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What do the 'Betweensies' refer to?
What do the 'Betweensies' refer to?
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Study Notes
Linear Equations and Functions
- Equation of a line: y = mx + b, where m represents the slope and b represents the y-intercept.
- Slope is defined as the ratio of rise (change in Y) over run (change in X).
- Point-slope form of a line: y - y₁ = m(x - x₁), requiring a known point (x₁, y₁) and slope (m).
Arithmetic Sequences
- General formula: Aₙ = A₁ + (n - 1)d, where A₁ is the first term, d is the common difference, and n is the term number.
- Example: In the sequence 3, 5, 7, 9..., A₅₀ = 3 + (50 - 1)2 = 101.
Functions and Their Properties
- A function is defined by a mapping where arrows cannot split; this can be assessed using the vertical line test.
- A linear function maintains a consistent common difference in both X and Y values.
- Direct variation is expressed as y = kx, indicating a proportional relationship with no y-intercept.
Types of Lines
- Vertical lines take the form x = constant, representing all points where x equals the constant, thus not considered a function.
- Horizontal lines take the form y = constant and are classified as functions, where all y values remain the same.
Systems of Equations
- A system consists of two equations that share a common ordered pair.
- Methods to solve include substitution and elimination.
Additional Concepts
- "Betweensies" are expressed as #≤x≤# and #≤y≤#, defining constraints within a specified range.
- Lines of fit in scatter plots connect central dots to illustrate trends.
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Description
Test your knowledge of key algebra concepts with these study cards. Each card includes important definitions and formulas related to algebra, such as the slope-intercept form and arithmetic sequences. Perfect for students preparing for end-of-course assessments in Algebra 1.
