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Chapter 3: Problem 26

Graph each ordered pair on the same coordinate system. Label the axes; write a scale for each axis. \((-6,0)\)

Short Answer

Expert verified
Plot the point at (-6, 0) on the x-axis.

Step by step solution

01

Set Up the Coordinate System

Draw the x-axis (horizontal) and the y-axis (vertical). Make sure to label the x-axis with 'x' and the y-axis with 'y'.
02

Label the Scales

Decide on a scale for each axis. For example, each grid line can represent 1 unit. Label the numbers along the x-axis and y-axis accordingly. Ensure that both positive and negative values are included.
03

Plot the Point (-6, 0)

Identify the coordinates (-6, 0). Move 6 units to the left along the x-axis to reach -6. Since the y-coordinate is 0, do not move up or down. Place a point at the intersection of x = -6 and y = 0.
04

Label the Point

Once you have plotted the point, label it with the coordinates (-6, 0) next to the point.

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Key Concepts

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

Coordinate System
A coordinate system is a grid made up of two perpendicular lines called axes. The horizontal line is the x-axis and the vertical line is the y-axis. Where they intersect is called the origin, marked (0,0). Coordinate systems help us to locate points on a plane.

There are two main parts:
  • **x-axis**: This is the line running horizontally, from left to right.
  • **y-axis**: This is the line running vertically, from bottom to top.
Each point on the plane can be described by an ordered pair \((x, y)\), where \x\ represents the horizontal position and \y\ represents the vertical position.
When setting up the coordinate system, make sure to label each axis and include positive and negative values. This helps in accurately locating and plotting points.
Plotting Points
Plotting points is the process of placing a point on the coordinate plane at a specific location determined by coordinates \((x, y)\). Follow these steps to plot a point:

1. Start from the origin (0,0).
2. Move horizontally along the x-axis to the x-coordinate.
3. From there, move vertically to the y-coordinate.
4. Mark the point at the intersection.

For example, to plot the point (-6, 0):
  • Start at the origin.
  • Move 6 units to the left along the x-axis to reach -6.
  • Since the y-coordinate is 0, you stay on the x-axis.
  • Place a point where x = -6 and y = 0.

Remember, always move horizontally first and then vertically!
Scales on Axes
Scales on axes ensure we can accurately plot points. It鈥檚 essential to decide on a scale before plotting points. The scale is simply the value each grid line represents. Common scales include 1 unit for each grid line, but you can use different scales depending on your data.

Follow these tips when labeling scales:
  • Make sure the intervals are consistent along each axis.
  • Label both positive and negative values on the x-axis and y-axis.
  • Choose a scale that matches the range of your data.
For example, if we choose 1 unit per grid line:
  • You will label the x-axis from ... -3, -2, -1, 0, 1, 2, 3 ...
  • Similarly, label the y-axis from ... -3, -2, -1, 0, 1, 2, 3 ...
    • This approach makes it easier to accurately plot and read points on the graph.
    Labeling Points
    Labeling points means writing down the coordinates of each point next to it on the graph. This helps in identifying what each point represents. After you plot a point:

    鈥� Write the coordinates in parentheses right next to the point. For example, (3, -2).
    鈥� Use a clear and readable font size to avoid confusion.
    鈥� Make sure the label does not overlap with other points or lines.

    Labeling ensures anyone reading the graph can understand the location of each plotted point without second-guessing. For the point (-6, 0), label it as \((-6, 0)\) right next to the plotted point on the graph.

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