can we start drawing the line graph from any point on the graph or should we start from the point on the axis itself?
Points on a Graph
Objectives
After reviewing this unit you will be able to:
- Identify the x and y axes.
- Identify the origin. on a graph.
- Identify x and y coordinates of a point.
- Plot points on a graph.
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.
|
|
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:
At the right is a graph with two points, B and D. In this figure:
|
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:
Looking back at the graph with our points B and D, we now identify the y-coordinate for each.
|
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 ycoordinate for each of the points B and D.
|
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 C--If you look at how far the point is from the origin along the y-axis, the answer is zero. Therefore, the y-coordinate is zero. Any point that lies on the x-axis has a y-coordinate of zero.
If you move along the x-axis to find the x-coordinate, the point is 200 from the origin. The coordinates of point C are (200, 0)
Example
|
Answers to Example
- Which point is on the y-axis? Point A
- Which point is labeled (20, 60)? Point B
- 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 thex-coordinate of the point. In our example, this is at 200. | Then, draw a line extending out from the y-axis at they-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). |
hope you get it an also learned new things about graphs.