Problem 4 - Prealgebra

Question

Graph each of the following ordered pairs. $$(-4,-2)$$

Step-by-Step Solution

Answer

Plot the point \\((-4, -2)\\) by moving left 4 units and down 2 units from the origin.

Step 1: Understand the Coordinate Plane

The coordinate plane is made up of two axes: the x-axis (horizontal) and the y-axis (vertical). Each point on the plane is represented by an ordered pair \((x, y)\) where \(x\) denotes the position along the x-axis and \(y\) denotes the position along the y-axis.

Step 2: Identify the Ordered Pair

The ordered pair given is \((-4, -2)\). This means you need to move to \(-4\) on the x-axis and \(-2\) on the y-axis.

Step 3: Plot the x-coordinate

Start at the origin (0,0), and move 4 units to the left on the x-axis because the x-coordinate is \(-4\).

Step 4: Plot the y-coordinate

From the \(-4, 0)\) position (4 units to the left of the origin), move 2 units down on the y-axis because the y-coordinate is \(-2\).

Step 5: Mark the Point

Once you have moved according to both the x and y coordinates, place a dot at the position \((-4, -2)\) on the graph. This is the location of the ordered pair.

Key Concepts

Understanding Ordered Pairs

An ordered pair is a set of two numbers used to identify a point on the coordinate plane. It is written in the format \((x, y)\). The first number, named the x-coordinate, tells you how far to move horizontally from the origin, which is the point (0,0). The second number, the y-coordinate, tells you how far to move vertically.

• Ordered pairs are crucial for locating points precisely on a graph.
• The sequence is important: \((x, y)\) is not the same as \((y, x)\).

Visualizing ordered pairs helps in understanding how they plot onto the coordinate plane, forming the basis for more complex mathematical concepts like graphing shapes and solving equations.

The Role of the X-axis

The x-axis is one of the two axes that make up the coordinate plane, and it runs horizontally. It is the line where the y-coordinate is equal to zero. As part of ordered pairs, the x-coordinate tells you how far to move along this axis.

• Moving left from the origin means the x-coordinate is negative.
• Moving right from the origin means the x-coordinate is positive.

When you receive an ordered pair like \((-4, -2)\), the x-value, which is -4, indicates a movement of 4 units to the left on the x-axis. This knowledge helps us locate differing positions in horizontal terms efficiently.

Navigating the Y-axis

The y-axis complements the x-axis by providing vertical movement. It runs vertically in the coordinate plane and is the line where the x-coordinate is zero. In an ordered pair, the y-coordinate tells us how far to move along this axis.

• When moving upwards, the y-coordinate is positive.
• When moving downwards, it is negative.

In our ordered pair \((-4, -2)\), -2 represents the position on the y-axis. Starting from the x-coordinate position, we move down 2 units. Understanding the y-axis helps in aligning points correctly above or below the origin, completing the navigation needed to precisely plot a point on the coordinate plane.