Problem 15 - Prealgebra

Question

Graph each of the following ordered pairs. $$(2,0)$$

Step-by-Step Solution

Answer

Plot the point on the x-axis at (2,0) without moving up or down.

Step 1: Understanding the Ordered Pair

The ordered pair given is \((2, 0)\). In this pair, "2" is the x-coordinate and "0" is the y-coordinate. This means the point is located on the x-axis, 2 units to the right of the origin (since the y-coordinate is 0).

Step 2: Identify the Axes

On a graph, there are two axes: the horizontal axis, called the "x-axis," and the vertical axis, called the "y-axis." An ordered pair \((x, y)\) gives the position relative to these axes.

Step 3: Plot the x-coordinate

Find the value "2" on the x-axis, which is 2 units to the right of the origin, where the x-axis and y-axis meet at \((0,0)\).

Step 4: Plot the y-coordinate

Since the y-coordinate is "0," you will not move up or down from the x-axis point. Stay on the x-axis at the point \((2,0)\).

Step 5: Mark the Point

Mark the point on the graph at \((2, 0)\). This point is 2 units to the right along the x-axis and remains on the axis because the y-coordinate is zero.

Key Concepts

Understanding Ordered Pairs

An ordered pair, such as ((2, 0)), is a fundamental concept in graphing and mathematics. An ordered pair consists of two numbers written in a specific order, usually in the form ((x, y)). Each number in the pair has a distinct role:

• The first number corresponds to the x-coordinate.
• The second number corresponds to the y-coordinate.

The x-coordinate indicates how far left or right a point is from the origin on the x-axis. The y-coordinate tells you how far up or down a point is from the x-axis. In our case, with the ordered pair ((2, 0)), we have:

• x-coordinate: "2" means move 2 units to the right,
• y-coordinate: "0" means do not move up or down.

This ordered pair uniquely identifies a position on the plane, providing a clear location.

Exploring the Coordinate Plane

The coordinate plane is a two-dimensional space defined by two perpendicular axes: the x-axis and the y-axis. It serves as a playground for graphing points, lines, and mathematical functions. Here's a closer look at this important tool:

• The x-axis: This is a horizontal line where the value of y is zero.
• The y-axis: This is a vertical line where the value of x is zero.

Both axes intersect at a point called the origin, denoted by ((0,0)). This point is where both x and y are zero, serving as the starting point for measuring other points on the plane.

When working with a coordinate plane, we use the ordered pair ((x, y)) to determine a point's location. We start at the origin, move "x" units along the x-axis, and then "y" units along the y-axis. This straightforward mechanism scales up to more complex graphing tasks, providing a consistent approach to understanding spatial relationships.

Plotting Points on the Coordinate Plane

Plotting points is an essential skill for visualizing and interpreting data on the coordinate plane. Let's dive deeper into the process: To plot an ordered pair like ((2, 0)), follow these simple steps:

• Locate the x-coordinate: Begin at the origin ((0, 0)) and count 2 units to the right along the x-axis.
• Y-coordinate placement: Since the y-coordinate is "0," you stay at the level of the x-axis, not moving vertically.
• Mark the point: Once you've moved to the correct spot on the x-axis, put a mark to signify the point's location.

With practice, plotting becomes second nature, helping you solve math problems, understand graph-based data, and visualize mathematical concepts. Whether you're plotting a single point or a series of points, the clarity that comes from seeing these on a graph can provide powerful insights into the relationships between different variables.