Ordered Pairs

Definition

An ordered pair is a set of two numbers that represent a specific point on a coordinate plane. The first number in the pair represents the horizontal (x) coordinate, while the second number represents the vertical (y) coordinate. Ordered pairs are fundamental to graphing linear equations in two variables.

5 Must Know Facts For Your Next Test

1. Ordered pairs are written in the form $(x, y)$, where $x$ represents the horizontal position and $y$ represents the vertical position on a coordinate plane.
2. The coordinate plane is divided into four quadrants, with ordered pairs in the first quadrant having both positive $x$ and $y$ values.
3. Plotting ordered pairs on a coordinate plane allows you to visualize the relationship between the variables in a linear equation.
4. The slope of a linear equation can be calculated using the coordinates of two points on the line, represented by their ordered pairs.
5. Ordered pairs are essential for graphing the solutions to a system of linear equations in two variables.

Review Questions

• Explain how ordered pairs are used to represent points on a coordinate plane.
  • Ordered pairs are used to represent specific points on a coordinate plane by providing the horizontal (x) and vertical (y) coordinates of that point. The first number in the ordered pair, $x$, indicates the position along the horizontal axis, while the second number, $y$, indicates the position along the vertical axis. By plotting ordered pairs on the coordinate plane, you can visualize the relationship between the variables in a linear equation and determine the solutions to the equation.
• Describe how ordered pairs are used to calculate the slope of a linear equation.
  • The slope of a linear equation can be calculated using the coordinates of two points on the line, represented by their ordered pairs. The slope formula is $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the ordered pairs of the two points. By substituting the $x$ and $y$ coordinates of the ordered pairs into the slope formula, you can determine the slope of the line, which is a key characteristic of a linear equation.
• Explain the importance of ordered pairs in graphing systems of linear equations in two variables.
  • Ordered pairs are essential for graphing the solutions to a system of linear equations in two variables. By plotting the ordered pairs that satisfy each equation on the coordinate plane, you can visually represent the relationship between the variables and identify the point of intersection, which represents the solution to the system. The coordinates of this point of intersection are given by the ordered pair that satisfies both equations in the system, allowing you to determine the values of the variables that solve the system.

Related terms

Coordinate Plane:

A two-dimensional plane with horizontal (x-axis) and vertical (y-axis) axes, used to represent and plot ordered pairs.

Linear Equation:

An equation that represents a straight line and can be expressed in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Cartesian Coordinates:

A coordinate system that uses ordered pairs to locate points on a plane, with the horizontal coordinate (x) and vertical coordinate (y) defining the position.