# Pre-Algebra: Basic Graphing

The coordinate plane and points.
Graphs of lines.
Quiz on basic graphing.

## The Coordinate Plane and Points

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.

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

## Graphs of Lines

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!

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