Questions and Answers
What does the equation $y=mx+b$ represent?
What is the formula for Slope?
Rise over Run
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?
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A function cannot have an arrow that splits.
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What is the characteristic of a Linear Function?
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What type of line is represented by the equation $x=3$?
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What does the equation $y=2$ represent?
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Match the following terms with their definitions:
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What is the purpose of a Line of Fit?
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What is the equation for Direct Variation?
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How can you determine a Direct Variation?
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What is a system of equations?
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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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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.