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Chapter 4: Problem 17

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

Short Answer

Expert verified
Plot the point at \((-2,0)\) on the x-axis.

Step by step solution

01

Understand the Ordered Pair

An ordered pair is written as \((x, y)\). The first number is the x-coordinate and the second number is the y-coordinate.
02

Locate the Position on the X-axis

For the point \((-2, 0)\), the x-coordinate is \(-2\). Start at the origin \((0,0)\) and move two units to the left on the x-axis because the x-coordinate is negative.
03

Locate the Position on the Y-axis

For this ordered pair, the y-coordinate is \(0\). This means you stay at the same level on the y-axis, not moving up or down from the x-axis.
04

Mark the Point on the Graph

From the position \((-2, 0)\) on the x-axis, draw a small point or dot. The point is located directly on the x-axis at \(x = -2\).
05

Verify the Point

Ensure that the point is plotted correctly by checking the coordinates. You should see a point positioned at \(-2\) on the x-axis aligning with \(0\) on the y-axis.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

The x-axis and y-axis
The x-axis and y-axis are fundamental components of the coordinate plane, a two-dimensional space used in graphing. They intersect at a point called the origin, denoted as \(0,0\).
  • The x-axis is the horizontal line. It runs left to right and is used to plot the x-coordinate of a point. Negative values lie to the left of the origin, while positive values extend to the right.
  • The y-axis is the vertical line. It runs up and down and is used for the y-coordinate. Points above the origin are positive, and those below are negative.
Together, these axes create a framework that allows for precise plotting and reading of points, helping us to visualize data in a structured way.
Plotting Points
Plotting points on a coordinate plane involves identifying the specific location of an ordered pair \(x, y\). This easy-to-understand process involves a few simple steps:
  • Start at the Origin: All points are plotted from the origin at \(0,0\). This serves as the starting point for locating any ordered pair.
  • Move Horizontally: To plot the x-coordinate, move left or right along the x-axis based on whether the x-value is negative or positive.
  • Move Vertically: From the x-position, move up or down along the y-axis according to the y-coordinate. If it is zero, remain at the x-position on the x-axis.
  • Mark the Point: Once you鈥檝e located the correct position on both axes, draw a small dot to mark the point.
Plotting points allows us to see the relationship between the x and y coordinates, bringing mathematical concepts into a visual form.
Understanding the Coordinate Plane
The coordinate plane is a flat surface divided by the x-axis and y-axis, creating four sections called quadrants. Each point on the plane is represented by an ordered pair \(x, y\), indicating its position.
  • Quadrants: The coordinate plane has four quadrants, each with different signs for coordinates. The first quadrant contains positive x and y values, the second has negative x and positive y, the third includes negatives of both, and the fourth has positive x and negative y.
  • Reading Coordinates: The first value in the ordered pair is the x-coordinate, indicating horizontal position. The second value is the y-coordinate, indicating vertical position.
  • Graphical Representation: By plotting points on this plane, we can visualize relationships between numbers and functions, improving our understanding of geometry and algebra.
The coordinate plane is a powerful tool in mathematics, used in everything from simple graphing exercises to complex data analysis.

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