(x, y)

Definition

(x, y) is a coordinate pair that represents a specific point on a two-dimensional coordinate plane. The x-coordinate indicates the horizontal position, while the y-coordinate indicates the vertical position of the point. This term is fundamental to understanding the Rectangular Coordinate System and graphing linear equations in two variables.

5 Must Know Facts For Your Next Test

1. The $(x, y)$ coordinate pair uniquely identifies the location of a point on a two-dimensional coordinate plane.
2. The $x$-coordinate represents the horizontal distance from the origin (0, 0), while the $y$-coordinate represents the vertical distance from the origin.
3. Positive $x$-coordinates are to the right of the origin, and negative $x$-coordinates are to the left of the origin.
4. Positive $y$-coordinates are above the origin, and negative $y$-coordinates are below the origin.
5. The coordinates $(x, y)$ can be used to graph linear equations in two variables on the Cartesian coordinate plane.

Review Questions

• Explain how the $(x, y)$ coordinate pair is used to locate a point on the Cartesian coordinate plane.
  • The $(x, y)$ coordinate pair is used to uniquely identify the location of a point on the Cartesian coordinate plane. The $x$-coordinate represents the horizontal distance from the origin (0, 0), while the $y$-coordinate represents the vertical distance from the origin. By specifying the $x$ and $y$ values, you can precisely locate a point on the two-dimensional grid, allowing you to graph points, lines, and other geometric shapes.
• Describe how the $(x, y)$ coordinate pair is used to graph linear equations in two variables.
  • The $(x, y)$ coordinate pair is essential for graphing linear equations in two variables on the Cartesian coordinate plane. Linear equations in two variables are of the form $ax + by = c$, where $a$, $b$, and $c$ are real numbers, and $x$ and $y$ are the variables. To graph a linear equation, you can substitute different values for $x$ and solve for the corresponding $y$-values, creating a set of $(x, y)$ coordinate pairs that lie on the line. By plotting these points on the coordinate plane, you can visualize the linear relationship between the two variables.
• Analyze how the $(x, y)$ coordinate pair can be used to determine the slope and y-intercept of a linear equation in two variables.
  • The $(x, y)$ coordinate pair can be used to determine the slope and y-intercept of a linear equation in two variables. The slope of a line is given by the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. By substituting the $(x, y)$ coordinates of two points, you can calculate the slope, which represents the rate of change between the variables. Additionally, the y-intercept of the line can be found by identifying the $y$-coordinate of the point where the line crosses the $y$-axis, which corresponds to the value of $c$ in the linear equation $ax + by = c$.

Related terms

Rectangular Coordinate System: A two-dimensional coordinate system where the position of a point is described by its horizontal (x) and vertical (y) coordinates.

Linear Equation in Two Variables: An equation of the form $ax + by = c$, where $a$, $b$, and $c$ are real numbers, and $x$ and $y$ are the variables.

Cartesian Coordinate Plane: A two-dimensional plane where the horizontal axis is the $x$-axis and the vertical axis is the $y$-axis, forming a grid of perpendicular lines.