Podcast
Questions and Answers
What is the definition of linear equations?
What is the definition of linear equations?
What is an example of the Slope Intercept Form?
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).
Point-slope form for linear equations is represented as y - y₁ = ____ (x - x₁).
m
Parallel lines are lines that eventually meet.
Parallel lines are lines that eventually meet.
Signup and view all the answers
What is the first step to graphing linear equations in slope-intercept form?
What is the first step to graphing linear equations in slope-intercept form?
Signup and view all the answers
What is the solution of the linear system mentioned?
What is the solution of the linear system mentioned?
Signup and view all the answers
Match the following exponent rules with their definitions:
Match the following exponent rules with their definitions:
Signup and view all the answers
According to the zero exponent rule, any base with an exponent of zero is equal to one.
According to the zero exponent rule, any base with an exponent of zero is equal to one.
Signup and view all the answers
An arithmetic sequence is a sequence of numbers such that the difference between _____ terms is constant.
An arithmetic sequence is a sequence of numbers such that the difference between _____ terms is constant.
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
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.
