Points on a Graph

Objectives
After reviewing this unit you will be able to:

Elements of a Graph

We often use graphs to give us a picture of the relationships between variables. Let's first look at the basic construction of graphs.

  • A graph is a visual representation of a relationship between two variables, x and y.
  • A graph consists of two axes called the x (horizontal) and y (vertical) axes. These axes correspond to the variables we are relating. In economics we will usually give the axes different names, such as Price and Quantity.
  • The point where the two axes intersect is called the origin. The origin is also identified as the point (0, 0).

Coordinates of Points

A point is the basic relationship displayed on a graph. Each point is defined by a pair of numbers containing two coordinates. A coordinate is one of a set of numbers used to identify the location of a point on a graph. Each point is identified by both an x and a y coordinate. In this unit you will learn how to find both coordinates for any point. You will also learn the correct notation for labeling the coordinates of a point. You will first begin by identifying the x-coordinateof a point.

Identifying the x-coordinate

The x-coordinate of a point is the value that tells you how far from the origin the point is on the horizontal, or x-axis. To find the x-coordinate of a point on a graph:
  • Draw a straight line from the point directly to the x-axis.
  • The number where the line hits the x-axis is the value of the x-coordinate.

At the right is a graph with two points, B and D. In this figure:

  • The x-coordinate of point B is 100.
  • The x-coordinate of point D is 400.

Identifying the y-coordinate

As we already mentioned, each point is defined by two coordinates, the x and the y coordinate. Now that you know how to find the x-coordinate of a point, you have to be able to find the y-coordinate. The y-coordinate of a point is the value that tells you how far from the origin the point is on the vertical, or y-axis. To find the y-coordinate of a point on a graph:
  • Draw a straight line from the point directly to the y-axis.
  • The number where the line hits the axis is the value of the y-coordinate.

Looking back at the graph with our points B and D, we now identify the y-coordinate for each.

  • The y-coordinate of point B is 400.
  • The y-coordinate of point D is 100.

Notation for Identifying Points

Once you have the coordinates of a point you can use the ordered pair notation for labeling points. The notation is simple. Points are identified by stating their coordinates in the form of (x, y). Note that the x-coordinate always comes first. For example, in the figure we've been using, we have identified both the x and y coordinate for each of the points B and D.
  • The x-coordinate of point B is 100.
  • The y-coordinate of point B is 400.
  • Coordinates of point B are (100, 400)
  • The x-coordinate of point D is 400.
  • The y-coordinate of point D is 100.
  • Coordinates of point D are (400, 100)

Points On The Axes

If a point is lying on an axis, you do not need to draw lines to determine the coordinates of the point. In the figure below, point A lies on the y-axis and point C lies on the x-axis. When a point lies on an axis, one of its coordinates must be zero.

  • Point A--If you look at how far the point is from the origin along the x-axis, the answer is zero. Therefore, the x-coordinate is zero. Any point that lies on the y-axis has an x-coordinate of zero.
     
    If you move along the y-axis to find the y-coordinate, the point is 400 from the origin. The coordinates of point A are (0, 400)

Example

  1. Which point is on the y-axis?
  2. Which point is labeled (20, 60)?
  3. Which point(s) have a y-coordinate of 30?

Answers to Example

  1. Which point is on the y-axis? Point A
  2. Which point is labeled (20, 60)? Point B
  3. Which point(s) have a y-coordinate of 30? Points A & C

 


[solution to example]

Plotting Points on a Graph

There are times when you are given a point and will need to find its location on a graph. This process is often referred to as plotting a point and uses the same skills as identifying the coordinates of a point on a graph. The process for plotting a point is shown using an example.

Example

Plot the point (200, 300).

Step One Step Two Step Three
First, draw a line extending out from the x-axis at the x-coordinate of the point. In our example, this is at 200. Then, draw a line extending out from the y-axis at the y-coordinate of the point. In our example, this is at 300. The point where these two lines intersect is at the point we are plotting, (200, 300).

You are now ready to try a practice problem. If you have already completed the first practice problem for this unit you may wish to try the additional practice.

       
[practice] [additional practice] [table of contents] [section one summary]