Basic Equations
Basic Graphing
Fractions

The coordinate plane and points
Graphs of lines
Quiz on 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.

• The origin's coordinates are (0,0).
• 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:

When graphing, the coordinate plane will be labeled with "tick marks" denoting the scale.  Beginning at the origin, 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!

However basic this seems, it is a necessary skill for graphing lines and other equations.

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

• 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.

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 process 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.

 ```1.   Graph:   y = 2x + 1      Solution:        y = 2(0) + 1      y = 1      (0,1)``` An x-coordinate of 0 was selected. The equation was solved for y. The resulting ordered pair is (0,1). ```     x | y      ---------      0 | 1      1 | 3      2 | 5      -1 |-1``` The process described above repeated 4 times. The results are shown to the left in table form.
The graph:

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

Math for Morons Like Us - Pre-Algebra: Basic Graphing
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