linear equation

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linear equation

A student graphs a linear equation on a coordinate plane.

Definition
  1. Noun:
    • A polynomial equation of the first degree: A mathematical statement where the highest power of the variable(s) is one. It represents a straight line when graphed on a coordinate plane.
Usage
  • The term "linear equation" is used to describe a specific type of algebraic equation. It is typically presented in forms such as (with one variable) or (with two variables), where , , and are constants.
  • It is a fundamental concept in algebra and coordinate geometry.
Examples
  • Noun:
    • Solving the linear equation 2x + 3 = 7 is a basic algebra skill.
    • The graph of every linear equation in two variables is a straight line.
    • We learned how to write a linear equation to represent a real-world situation.
Advanced Usage
  • System of linear equations: Refers to a collection of two or more linear equations involving the same set of variables.
    • We used matrices to solve the system of linear equations.
  • Linear equation in n variables: A more general form, , which describes a hyperplane in n-dimensional space.
    • The concept of a linear equation extends to any number of variables.
Variants and Related Words
  • Linear (adj): Of, relating to, or resembling a line; involving a single dimension. In mathematics, it describes an equation, function, or relationship that is of the first degree.
    • The relationship between distance and time at constant speed is linear.
  • Linearity (n): The quality or state of being linear.
  • Nonlinear equation (n): An equation in which the variable(s) are raised to a power other than one or appear in other nonlinear functions (e.g., ).
Synonyms
  • First-degree equation: A direct synonym emphasizing the highest power of the variable.
  • Linear polynomial equation: A more formal synonym specifying it is a polynomial of degree one.
Related Phrases
  • Slope-intercept form: A common way to express a linear equation in two variables: , where is the slope and is the y-intercept.
    • Convert the standard form equation into slope-intercept form to graph it easily.
  • Standard form: Another common representation for a linear equation in two variables: , where A, B, and C are integers.
    • The problem asked us to write the linear equation in standard form.
linear equation

A student graphs a linear equation on a coordinate plane.

Noun
  1. a polynomial equation of the first degree