key term - Ordered Pair

Definition

An ordered pair is a set of two numbers or coordinates that represent a specific point on a coordinate plane. The ordered pair is typically denoted as (x, y), where x represents the horizontal position and y represents the vertical position of the point.

5 Must Know Facts For Your Next Test

1. Ordered pairs are used to represent the location of a point on a coordinate plane, where the first number (x-coordinate) indicates the horizontal position and the second number (y-coordinate) indicates the vertical position.
2. The coordinates of an ordered pair can be positive, negative, or zero, depending on the quadrant in which the point is located on the coordinate plane.
3. Ordered pairs are essential for graphing linear equations, as each point on the graph corresponds to a unique ordered pair that satisfies the equation.
4. In the context of relations and functions, ordered pairs are used to represent the input and output values, where the first element is the independent variable (x) and the second element is the dependent variable (y).
5. When solving systems of linear equations with two variables, the solution is represented as an ordered pair that satisfies both equations simultaneously.

Review Questions

• Explain how ordered pairs are used to graph linear equations in two variables.
  • Ordered pairs are the fundamental building blocks for graphing linear equations in two variables. Each point on the graph of a linear equation corresponds to a unique ordered pair (x, y) that satisfies the equation. By plotting multiple ordered pairs that satisfy the equation, you can construct the graph of the linear equation, which will be a straight line. The x-coordinate of the ordered pair represents the horizontal position, while the y-coordinate represents the vertical position on the coordinate plane.
• Describe the role of ordered pairs in the context of relations and functions.
  • In the study of relations and functions, ordered pairs are used to represent the input and output values. The first element of the ordered pair is the independent variable (x), and the second element is the dependent variable (y). This relationship is denoted as (x, y), where x is the input and y is the corresponding output. Understanding the structure and interpretation of ordered pairs is crucial for identifying and analyzing the properties of relations and functions, such as domain, range, and function notation.
• Analyze how ordered pairs are used to solve systems of linear equations with two variables.
  • When solving a system of linear equations with two variables, the solution is represented as an ordered pair (x, y) that satisfies both equations simultaneously. The x-coordinate of the ordered pair represents the value of the first variable, and the y-coordinate represents the value of the second variable. To find the solution, you need to identify the unique ordered pair that makes both equations true, either through graphing, substitution, or elimination methods. The ordered pair solution is the point where the graphs of the two linear equations intersect, representing the values of the variables that satisfy the system.

Related terms

Coordinate Plane:

A two-dimensional plane with a horizontal x-axis and a vertical y-axis, used to represent and plot points and graphs.

Cartesian Coordinates: A system of spatial coordinates in which the position of a point on a plane is determined by its distance from two perpendicular axes, typically labeled x and y.

Graphing:

The process of representing mathematical relationships, functions, or data visually on a coordinate plane.