Podcast Beta
Questions and Answers
What is the form of a linear function?
What characterizes a linear equation?
Each term is either a constant or the product of a constant and a single variable.
What is a dependent variable?
A variable that is measured and affected during an experiment.
What is an independent variable?
Signup and view all the answers
What does the y-intercept represent?
Signup and view all the answers
What is an x-intercept?
Signup and view all the answers
What is the standard form of a line?
Signup and view all the answers
What describes the slope of a line?
Signup and view all the answers
What is the point-slope equation?
Signup and view all the answers
What is the slope-intercept form of a line?
Signup and view all the answers
Horizontal lines are parallel to the horizon.
Signup and view all the answers
Vertical lines are parallel to the horizon.
Signup and view all the answers
What are perpendicular lines?
Signup and view all the answers
What defines parallel lines?
Signup and view all the answers
An undefined slope corresponds to a vertical line.
Signup and view all the answers
A positive slope indicates a line that is decreasing.
Signup and view all the answers
A line with a negative slope trends upward from left to right.
Signup and view all the answers
A zero slope describes a horizontal line.
Signup and view all the answers
Study Notes
Linear Functions and Equations
- Linear functions have a graph represented by a straight line, expressed as y = f(x) = a + bx.
- A linear equation is an algebraic equation where each term is either a constant or a product of a constant with a single variable raised to the first power.
Variables
- The dependent variable is affected by changes in the independent variable and is what is measured during an experiment.
- The independent variable is changed by the scientist to observe its effect on the dependent variable, ensuring a fair test by only varying one independent variable at a time.
Intercepts
- The y-intercept (b) of a line is the value of y when the line crosses the y-axis in the linear equation y = mx + b.
- The x-intercept is the point on the graph where y equals zero.
Line Representations
- Standard form of a line is represented as Ax + By = C, where A is a positive integer, and B and C are integers.
- Slope (m) indicates the steepness and direction of a line, with definitions for increasing, decreasing, horizontal, or vertical slopes.
Equation Forms
- Point-slope form of a linear equation is y − y1 = m(x − x1), using a known point on the line (x1, y1) and the slope (m).
- Slope-intercept form is given as y = mx + b, highlighting the slope and the y-intercept.
Line Characteristics
- Horizontal lines run from left to right and are parallel to the horizon, defined as having a zero slope.
- Vertical lines are perpendicular to the horizon and have an undefined slope due to the invariant x-coordinate, creating no "run."
- Perpendicular lines intersect at right angles, while parallel lines never intersect or touch.
Slope Types
- A positive slope indicates an increasing line, while a negative slope indicates a decreasing line.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge with these flashcards on Linear Functions and Linear Equations from Algebra 2 Chapter 2. Understand the definitions and forms of linear relationships. Perfect for studying and reinforcing key concepts in algebra.