Problem 2 - Algebra 1: Concepts and Skills

Question

In Exercises \(1-3,\) complete the sentence. In the ordered pair (2, 5), the y-coordinate is _____.

Step-by-Step Solution

Answer

The y-coordinate of the ordered pair (2, 5) is 5.

Step 1: Identify the Ordered Pair

The question gives an ordered pair (2, 5). This is a set of two numbers in a specific order where the first number is the x-coordinate and the second number is the y-coordinate.

Step 2: Identify the Y-Coordinate

In the ordered pair (2,5), the second term or number is the Y-coordinate. So in this case, the Y-coordinate is 5.

Key Concepts

Coordinates

Coordinates help us identify precise locations on a plane. They are usually represented by ordered pairs, such as \((x, y)\). This means that any point on a flat surface can be located using two values, one for each direction.

• The first number in the pair represents the position along the horizontal axis, known as the x-axis.
• The second number shows the position along the vertical axis, called the y-axis.

Ordered pairs are crucial in math because they help in plotting points on a graph, which is essential for visualizing mathematical functions and data.
The ordered pair must be read in a specific sequence (x first, then y). This order distinguishes one point from another by their placements in a two-dimensional space.

X-Coordinate

The x-coordinate in an ordered pair represents a point's position on the horizontal axis (x-axis) of a coordinate plane. In any ordered pair \((x, y)\), the x-coordinate is always the first value.

• Think of the x-coordinate as the left-right value. If x is negative, the point is to the left of the origin.
• If x is positive, the point is to the right of the origin.

An easy way to remember is that 'x' comes before 'y' in the alphabet, so it makes sense that it appears first in an ordered pair. Knowing the x-coordinate allows you to determine one aspect of a point's position relative to the center of the graph, called the origin \((0, 0)\).
Using x-coordinates, you can quickly gauge how far along the horizontal line a point lies, making it pivotal in plotting graphs.

Y-Coordinate

The y-coordinate in an ordered pair shows where a point is positioned along the vertical axis (y-axis) of the graph. In the order of an ordered pair \((x, y)\), this is always the second number.

• Visualize the y-coordinate as the up-down value. A positive y-value indicates the point is above the origin.
• A negative y-value means the point is below the origin.

Unlike the x-coordinate, the y-coordinate focuses on vertical placement. It's crucial for determining elevation above or below the origin point on a graph.
By knowing both the x and y coordinates, you're able to pinpoint a location on a two-dimensional plane precisely. The y-coordinate, as seen in the example of an ordered pair \((2, 5)\), is 5, meaning the point lies five units vertically from the origin.