Questions and Answers
What is the slope formula?
(Y2-Y1)/(X2-X1)
What is the slope-intercept form?
y=mx+b
What is the standard form of a linear equation?
Ax + By = C
What is the point slope form?
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What is the vertex form of a quadratic function?
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What is the slope of the line that passes through the points (-4,6) and (8,-2)?
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What is the slope of the line that passes through the points (2,5) and (4,6)?
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What is the slope of a vertical line?
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How is the equation for a vertical line written?
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What is the slope of a horizontal line?
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How is the equation for a horizontal line written?
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What is the slope of a line parallel to y = 1/2x - 3?
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What is the slope of a line perpendicular to y = 1/2x - 3?
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What is the y-intercept for the line y = -4x + 6?
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What is the slope for the line y = -4x + 6?
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What is the y-intercept for the line 6x + 3y = 12?
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What is the x-intercept for the line 6x + 3y = 12?
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What does the solution of a system of equations mean?
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What does it mean if a system of equations does not have a solution?
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What does it mean if a system of equations has an infinite amount of solutions?
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If you are writing a system of equations to represent the number of tickets sold at a concert, what will your two systems represent?
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How do you write 'The length is 3 less than 5 times the width' as a mathematical expression?
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How do you write 'The length is 2 less than 1/2 the width' as a mathematical expression?
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What is the equation for the perimeter of a rectangle with a perimeter of 25 in. and the length is 3 less than 4 times the width?
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What is the equation for the perimeter of a rectangle with a perimeter of 15 in. and the length is 1 less than 1/3 the width?
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Describe what standard form is in regards to polynomials.
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What is the term for a polynomial with a degree of 1?
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What is the term for a polynomial with a degree of 2?
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What is the term for a polynomial with a degree of 3?
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What is the term for a polynomial with a degree of 4?
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What is the term for a polynomial with one term?
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What is the term for a polynomial with two terms?
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What is the term for a polynomial with three terms?
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What is the equation for the area of a rectangle?
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What is the greatest common factor of 16x - 12?
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What is the greatest common factor of 15xyz + 10xy - 25xz?
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Would you shade above or below the line to represent possible solutions for Y > 3x?
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Study Notes
Key Algebra Concepts
- Slope Formula: The slope of a line defined as ( \frac{Y2 - Y1}{X2 - X1} ).
- Slope Intercept Form: A linear equation represented as ( y = mx + b ), where ( m ) is the slope and ( b ) is the y-intercept.
- Standard Form: Linear equations written in the format ( Ax + By = C ).
- Point Slope Form: Equation of a line expressed as ( y - y1 = m(x - x1) ).
- Vertex Form: Quadratic functions shown in the format ( y = a(x - h) + k ).
Slope Calculations
- Slope of Line through points (-4,6) and (8,-2): Calculated to be 1.
- Slope of Line through points (2,5) and (4,6): Slope equals ( \frac{1}{2} ).
- Vertical Line Slope: The slope is undefined; its equation is of the form ( x = \text{constant} ).
- Horizontal Line Slope: The slope equals 0; its equation is of the form ( y = \text{constant} ).
Line Relationships
- Parallel Lines: Lines with the same slope (e.g., slope of ( y = \frac{1}{2}x - 3 ) is ( \frac{1}{2} )).
- Perpendicular Lines: Lines that have slopes that are negative reciprocals (e.g., perpendicular slope to ( y = \frac{1}{2}x - 3 ) is -2).
- Y-Intercept Calculation: For ( y = -4x + 6 ), the y-intercept is 6.
- Slope Calculation: For ( y = -4x + 6 ), the slope is -4.
Systems of Equations
- Intersection Point Meaning: The point where two lines intersect represents the solution of a system of equations.
- No Solution Scenario: When lines are parallel, indicated by their slopes being equal, they do not intersect.
- Infinite Solutions Scenario: Occurs when both lines are identical, represented by the same equation.
Mathematical Expressions
- Ticket Sales Representation: Two equations can model ticket count and pricing for a concert.
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Length vs. Width Expressions:
- "Length is 3 less than 5 times the width": ( L = 5W - 3 )
- "Length is 2 less than ( \frac{1}{2} ) of the width": ( L = \frac{1}{2}W - 2 )
Perimeter Equations
- Perimeter Equation for Rectangle (P = 25 in., L = 3 less than 4W): ( 25 = 2W + 2(4W - 3) ).
- Perimeter Equation for Rectangle (P = 15 in., L = 1 less than ( \frac{1}{3} )W): ( 15 = 2W + 2(\frac{1}{3}W - 1) ).
Polynomial Terminology
- Standard Form in Polynomials: Arrangement from highest to lowest degree.
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Degrees of Polynomials:
- Degree 1: Linear
- Degree 2: Quadratic
- Degree 3: Cubic
- Degree 4: Quartic
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Types of Polynomials:
- One-term: Monomial
- Two-terms: Binomial
- Three-terms: Trinomial
Areas and Common Factors
- Area of Rectangle: Given by the formula ( \text{Length} \times \text{Width} ).
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Greatest Common Factor:
- For ( 16x - 12 ): GCF is 4.
- For ( 15xyz + 10xy - 25xz ): GCF is ( 5x ).
Graphing Solutions
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Shading Regions:
- For ( Y > 3x ): Shade above the line to represent feasible solutions.
- Other inequalities will similarly dictate where to shade based on their respective boundaries.
Studying That Suits You
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Description
Prepare for your Algebra 1B final exam with this comprehensive study set of flashcards. Each card covers key formulas and definitions, including slope formulas and various line forms to solidify your understanding of essential concepts. Test your knowledge and ensure you're ready for the exam.