Problem 18 - Prealgebra

Question

Graph each ordered pair on a coordinate system. $$N\left(4 \frac{1}{2}, 0\right)$$

Step-by-Step Solution

Answer

The point N(4.5, 0) is located on the x-axis at 4.5.

Step 1: Identify the Ordered Pair

The ordered pair given is \( N(4 \frac{1}{2}, 0) \). This means the first element, 4.5, represents the x-coordinate and the second element, 0, represents the y-coordinate.

Step 2: Draw the Coordinate Axes

Begin by drawing a horizontal line for the x-axis and a vertical line for the y-axis. Make sure to label the axes with 'x' and 'y' respectively, and include evenly spaced tic marks along each axis.

Step 3: Locate the x-coordinate

On the horizontal x-axis, move to the right from the origin 0 to the x-coordinate 4.5. This is the first part of the ordered pair and indicates how far you move along the x-axis.

Step 4: Locate the y-coordinate

Since the y-coordinate is 0, you do not need to move up or down from the x-axis. You remain at the point directly above (or below) the location 4.5 on the x-axis.

Step 5: Plot the Point

Mark a point on the graph at the coordinate (4.5, 0). Since the y-coordinate is 0, the point lies precisely on the x-axis.

Key Concepts

Graphing Ordered Pairs

To understand how to graph ordered pairs, let's delve into what these pairs represent. An ordered pair is essentially a set of two numbers written in a specific order, typically enclosed in parentheses like this: \(x, y\). These numbers signify positions on a graph and are used to depict points on a coordinate plane. The first number is what we call the x-coordinate, and it tells us how far left or right to move on the graph.
The second number is the y-coordinate and shows us how far up or down we need to go.
Graphing ordered pairs involves two main steps:

• Locate the position on the x-axis (using the first number).
• Locate the position on the y-axis (using the second number).

Once these positions are identified, you mark the point where they intersect. This is how an ordered pair like \(4.5, 0\) is represented visually on a two-dimensional plane.

X-Axis and Y-Axis

The x-axis and y-axis are crucial elements of a coordinate plane. Picture them as imaginary lines that cross at a point called the origin, denoted by \(0,0\). The x-axis stretches horizontally across the plane, while the y-axis extends vertically.
Together, these axes form a grid that allows us to plot points and navigate the space with precision.
Here's a bit more detail on each:

• The x-axis: The centerline that runs horizontally. Positive numbers are typically to the right, and negative numbers are to the left of the origin.
• The y-axis: This line goes up and down. Positive numbers head upwards, while negative numbers point downwards from the origin.

It's important to always label these axes clearly to avoid confusion when plotting points. Tic marks along these axes help in finding exact positions for the coordinates you need to plot.

Plotting Points

Plotting points on a coordinate plane is an engaging act of translating numbers into visual representations. With a pair of coordinates \(x, y\), you are essentially told a very specific location on the grid. We'll walk through the process of how to accurately plot a point like \(4.5, 0\).
Step-by-step guide:

• Start at the origin \(0,0\). This is where the x-axis and y-axis meet.
• Move horizontally along the x-axis to the right until you reach the first number, 4.5, in your ordered pair. This is the x-coordinate.
• Since the y-coordinate is 0, you don't need to move up or down from where you landed on the x-axis. Simply stay put.
• Mark this point with a small dot and you have successfully plotted your point on the graph.

Each point you plot provides a snapshot of a relationship between two numerical values, showcased on the graph where the x and y intersect.