Questions and Answers
What is the definition of linear equations?
What is an example of the Slope Intercept Form?
y = 4x + 3
Point-slope form for linear equations is represented as y - y₁ = ____ (x - x₁).
m
Parallel lines are lines that eventually meet.
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What is the first step to graphing linear equations in slope-intercept form?
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What is the solution of the linear system mentioned?
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Match the following exponent rules with their definitions:
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According to the zero exponent rule, any base with an exponent of zero is equal to one.
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An arithmetic sequence is a sequence of numbers such that the difference between _____ terms is constant.
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Study Notes
Linear Equations
- Defined as an equation involving two variables that produces a straight line when graphed.
Slope Intercept
- The format y = mx + b where m represents the slope and b is the y-intercept.
- Example: In y = 4x + 3, the slope is 4 and the y-intercept is 3.
Point-Slope Form
- Expressed as y - y₁ = m(x - x₁), focusing on the slope of the line and a known point on the line.
Parallel and Perpendicular Lines
- Parallel lines do not intersect in a plane.
- Perpendicular lines intersect at a 90° angle.
Graphing Linear Equations in Slope-Intercept Form
- Start by identifying the y-intercept and plotting the point.
- Use the slope to find a second point, then draw the line connecting the two points.
Graphing Using Intercepts
- Involves writing a linear equation in standard form to identify intercepts for graphing.
Solving Systems of Equations
- Use substitution by replacing one variable with its equivalent from another equation.
- Example solution: (1, 6) can be obtained via this method.
Solving by Substitution
- First, rearrange one equation to isolate a variable.
- Substitute the found value into another equation to solve for the remaining variable.
Solving by Elimination
- Create equations with matching coefficients for a variable to eliminate it.
- Solve for the remaining variable, then substitute back to find the other variable.
Exponents
- Represents the power to which a base number or expression is raised, usually shown as a superscript.
Product to Power Rule
- Simplifying involving multiplications with exponents by adding the exponents of like bases.
Quotient to Power Rule
- When dividing terms with the same base, subtract the exponents of the base.
Power to Power
- The dimension of power relates to energy over time, with the standard unit being Watts.
Negative Exponents
- A negative exponent indicates reciprocal; move the base to the opposite side of the fraction line and change the exponent to positive.
Zero Exponent Rule
- Any base raised to the power of zero equals one.
Polynomials
- Defined as expressions with more than two algebraic terms, comprising variables raised to various powers.
Multiplying Polynomials
- Multiply coefficients, and add exponents of like bases; after distribution, combine like terms.
Factoring Polynomials
- Involves identifying and extracting common factors from polynomial expressions.
Sequences
- A structured order of related events or items following one another.
Arithmetic Sequences
- A sequence where the difference between consecutive terms remains constant.
- Example: 5, 7, 9, 11, 13, ... presents a common difference of 2.
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Description
Explore key concepts from Algebra 1 with these helpful flashcards. Learn about linear equations, slope intercept form, and point-slope form. Perfect for quick study sessions and reviewing important algebraic principles.
