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.

Noun

1. a polynomial equation of the first degree