# Algebra: Graphing on the Coordinate Plane

On this page we hope to clear up problems that you might have with graphing on the coordinate plane.  Coordinate planes are used extensively throughout math and math related subjects (such as physics).  They are most useful when you need to graph an equation.

Read on or follow the links below to start understanding how to graph on the coordinate plane!

Graphing points
Graphing lines
Topics related to graphing
Quiz on graphing on the coordinate plane

## Graphing Points

Because graphing points on a coordinate plane is usually covered in the typical pre-algebra course, we followed that tradition on this site.  You can follow this link to better understand that area of graphing.

## Graphing Lines

In this section we will help you understand how to graph lines on a coordinate plane.

Most pre-algebra courses cover how to graph simple equations such as the following: y = 2x + 1.  So we followed the tradition on this site.  You can follow this link to better understand that area of graphing.

In math, a line is defined to be of infinite length and consisting of at least 2 points.  All lines are straight (a line is straight — a curve is curved).

When you need to graph an equation such as y = -(1/2)x + 2, the only thing you need to be especially wary of is the fraction.  Since a line consists of two or more points, all you need to do is find two or more ordered pairs that solve the equation.  The easiest way to do this is to draw a table such as the following and fill it in:

```     ---------
x | y
---------
0 |
2 |
4 |
```
You plug the x-values into the equation and find the y-values.  That gives you ordered pairs that you can graph on the coordinate plane and then "connect" into a line.

Example:

```1. Graph:    y = -.5x + 2
Solution: Begin by making a table (choose convenient
values for x).

------------------
| x | 0 | 2 | -2 |
------------------
| y |   |   |    |
------------------

Now plug the x-values into the original equation
and find the values for y.

y = -.5(0) + 2
y = 2

y = -.5(2) + 2
y = 1

y = -.5(-2) + 2
y = 3

Complete the table.

------------------
| x | 0 | 2 | -2 |
------------------
| y | 2 | 1 |  3 |
------------------

Now graph the points and draw a line by
"connecting the dots."  (Aren't you overwhelmed
by all this fun?)  The graph: Example Graph
```
The most confusing types of lines are lines that are either horizontal or vertical.  These are lines that are representative of an equation that has either an x variable or a y variable, but not both.

An equation such as y = 2 says that no matter what you plug in for y, you get 2.

An equation such as x = 4 has two things to keep in mind.  First of all, it has no slope!  This is because it is vertical.  (With a horizontal line, the slope is zero, but with a vertical line, the slope is undefined, so the line therefore has no slope.)  The other thing to remember is that no matter what you plug in for x, you'll get 4.

Example:

```1. Graph:    y = 2
Solution: The equation indicates that all the y
coordinates to be graphed are 2.  Pick any
two ordered pairs with 2 as the y coordinate
and graph.

The graph: Example Graph
```

## Topics Related to Graphing

Below are a couple of links to pages that discuss topics related to graphing, such as finding solutions to systems of equations.  They are not covered on this page in the spirit of convenience.  :-)  If it's not convenient, you could complain, and we might listen.  :-)

Finding the solutions to systems of equations by graphing.
Writing the equation of the graph of a line.

Take the quiz on graphing on the coordinate plane.  The quiz is very useful for either review or to see if you've really got the topic down.

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Math for Morons Like Us -- Algebra: Graphing on the Coordinate Plane
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