🎧 New: AI-Generated Podcasts Turn your study notes into engaging audio conversations. Learn more

Algebra 2 Chapter 2 Flashcards
18 Questions
100 Views

Algebra 2 Chapter 2 Flashcards

Created by
@GoldNeon

Podcast Beta

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the form of a linear function?

  • y = f(x) = a + bx (correct)
  • y = kx + c
  • y = Ax + By = C
  • y = mx + b
  • 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?

    <p>The variable that is changed by the scientist in an experiment.</p> Signup and view all the answers

    What does the y-intercept represent?

    <p>The value of y at the point where the line crosses the y-axis.</p> Signup and view all the answers

    What is an x-intercept?

    <p>A point on the graph where y is zero.</p> Signup and view all the answers

    What is the standard form of a line?

    <p>Ax + By = C</p> Signup and view all the answers

    What describes the slope of a line?

    <p>A number that describes both the direction and the steepness of the line.</p> Signup and view all the answers

    What is the point-slope equation?

    <p>(y - y1) = m(x - x1)</p> Signup and view all the answers

    What is the slope-intercept form of a line?

    <p>y = mx + b</p> Signup and view all the answers

    Horizontal lines are parallel to the horizon.

    <p>True</p> Signup and view all the answers

    Vertical lines are parallel to the horizon.

    <p>False</p> Signup and view all the answers

    What are perpendicular lines?

    <p>Lines that intersect at right angles.</p> Signup and view all the answers

    What defines parallel lines?

    <p>Lines that do not intersect or touch at any point.</p> Signup and view all the answers

    An undefined slope corresponds to a vertical line.

    <p>True</p> Signup and view all the answers

    A positive slope indicates a line that is decreasing.

    <p>False</p> Signup and view all the answers

    A line with a negative slope trends upward from left to right.

    <p>False</p> Signup and view all the answers

    A zero slope describes a horizontal line.

    <p>True</p> 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.

    Quiz Team

    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.

    Use Quizgecko on...
    Browser
    Browser