Problem 14 - Prealgebra

Question

Graph each ordered pair on a coordinate system. $$D(1,8)$$

Step-by-Step Solution

Answer

Graph the point by moving 1 unit right and 8 units up from the origin, then mark and label it as \(D\).

Step 1: Understanding the Coordinate System

To graph an ordered pair, familiarize yourself with the coordinate system, which includes the x-axis (horizontal) and the y-axis (vertical). The intersection of these axes is called the origin, represented by the point (0,0).

Step 2: Identify the Coordinates

Each ordered pair consists of two numbers: the first number is the x-coordinate and the second number is the y-coordinate. For the ordered pair \(D(1, 8)\), the x-coordinate is 1 and the y-coordinate is 8.

Step 3: Locate the X-coordinate

Begin by locating the x-coordinate on the x-axis. Since the x-coordinate is 1, find the point that lies 1 unit to the right of the origin along the x-axis.

Step 4: Locate the Y-coordinate

From the point you found on the x-axis, move vertically until you find the y-coordinate. Since the y-coordinate is 8, move 8 units up from the x-coordinate point.

Step 5: Plot the Ordered Pair

After locating both coordinates, mark the point where these movements intersect on the graph. This point represents the ordered pair \(D(1,8)\). Ensure it is clearly plotted.

Step 6: Label the Point

Label the point you plotted on the graph as \(D\) to indicate the specific ordered pair was graphed.

Key Concepts

Coordinate System

A coordinate system is a method for locating points using numbers. It comprises two perpendicular lines called axes. The horizontal line is known as the x-axis, while the vertical one is called the y-axis. These lines intersect at the center, which is the origin, marked as the point (0,0). The coordinate system is foundational in graphing because it provides a structure to position points in a two-dimensional space. The origin is important because it is the starting point for measuring distance along the axes. Understanding this system helps us precisely plot or locate any point given an ordered pair. By using this system, even abstract numbers become visually approachable and understandable.

X-axis and Y-axis

The x-axis and y-axis in a coordinate plane help define the position of a point. The x-axis runs horizontally, while the y-axis runs vertically. This perpendicular crossing creates four quadrants in the coordinate plane. Each axis serves as a reference line for measuring distances. The x-axis is used to determine the horizontal position of a point, measured in units to the left or right of the origin. Conversely, the y-axis measures the vertical position of a point in units above or below the origin. Together, these axes form the backbone of how coordinates are described, ensuring clarity and precision when plotting points on a graph.

Plotting Points

Plotting points is the process of placing a point on the coordinate plane using an ordered pair. An ordered pair consists of two numbers, enclosed in parentheses, separated by a comma. The first number of the ordered pair, the x-coordinate, tells how far to move horizontally from the origin along the x-axis.
- If the number is positive, you move right. - If it's negative, you move left.
The second number, the y-coordinate, indicates how far to move vertically. - A positive value means you move up. - A negative value means you move down.
By following this pattern, you can accurately place any point on the plane. This method makes visualizing mathematical concepts a lot simpler and is a crucial skill in graphing.

X-coordinate and Y-coordinate

Each point in a coordinate plane is defined by two values: the x-coordinate and the y-coordinate. The x-coordinate tells us how far and in which direction to move horizontally from the origin. It's the first number in our ordered pair, and its sign (positive or negative) indicates direction along the x-axis.
The y-coordinate, on the other hand, tells us how high or low the point is from the x-axis. It's the second number in the ordered pair. Its sign dictates whether you move upwards or downwards along the y-axis.
The structure provided by these coordinates allows for a precise location of points on the coordinate system, making it easier to interpret and analyze graphical data. Understanding x and y-coordinates is essential for mastering graphing and navigating through coordinate planes effectively.