Pre-Algebra: Basic Graphing

In the coordinate plane, or the rectangular coordinate system, the vertical y-axis and the horizontal x-axis intersect at a point called the origin.

This section will help you better understand the coordinate plane and how to graph points on the plane.
Throughout the tutorial, there are links to example graphs.  Follow these links, and your browser should allow you to download the example graphs to your hard drive where you can view them.

Important Things to Remember

• Points are named by an ordered pair.  Example:

       (4,2)

• The first number in an ordered pair is the x-coordinate, and the second number listed is the y-coordinate.  Example:

       Points Example Graph

The Tutorial
When graphing, the coordinate plane will be labeled with "tick marks" denoting the scale.  Beginning at the origion, count along the x-axis scale until you find the tick mark labeled with the x-axis coordinate of your point, and then count along the y-axis scale until you find the tick mark labeled with the y-axis coordinate of your point.  That is the location of your point!

Examples

Points Example
      

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This section will help you to understand how to better graph linear equations.

Important Things to Remember

• Linear equations can be graphed when in the form y = mx + b.
• m equals the slope of the line.
• b equals the point where the line crosses the y-axis.  This is called the y-intercept.

The Tutorial
When graphing linear equations, "plugging in points" is a suggested method of solving the equations and putting them in a graphical format.  To plug in points, select an x-coordinate (be reasonable in the number you select for the x-coordinate) and put the x-axis coordinate in the equation in place of x.  Then solve the equation.  This will give you a y-value.  Put your chosen x-value and the y-value you solved for together, and you will have an ordered pair (a point) that you can graph.  Repeat this proces about 4 or 5 times and then connect the points you have graphed.  The line you see will be the graph of a linear equation.

Examples

1.  Graph:    y = 2x + 1
    Solution:
    y = 2(0) + 1                 An x-coordinate of 0 was selected.
    y = 1                        The equation was solved for y.
    (0, 1)                       The resulting ordered pair is (0,1).

      x | y
    ---------
      0 | 1                      The process described above
      1 | 3                      repeated 4 times.  The results are
      2 | 5                      shown to the left in table form.
     -1 |-1

     The graph: Example Graph

Take the quiz on basic graphing.  (Very useful to review or to see if you've really got this topic down.)  Do it!