**Learning Objectives**

After completing this tutorial, you should be able to:

- Recognize when an equation in two variables is a linear equation.
- Graph a linear equation.

** Introduction**

In **Tutorial 20:
The Rectangular
Coordinate System**, we went over the basics of the rectangular
coordinate
system. In this tutorial we will be adding on to this by looking
at graphing linear equations by plotting points that are
solutions.
Basically, when you graph, you plot solutions and connect the dots to
get
your graph. Specifically,
when you graph linear equations, you will end up with a straight
line.
Let's see what you can do with these linear equations.

** Tutorial**

**Standard Form:**

**A x + By = C**

A linear equation in two variables is an equation that
can be written
in the form

A*x* + B*y* =
C,
where A and B are not both 0.

A

This form is called the **standard form of a linear
equation.**

If we subtract 5*x* from
both sides, then
we can write the given equation as -5*x* + *y* = -3.

**Since we can write it in the standard form, A x + By = C, then we have a linear
equation. **

If we were to graph this equation, we would end up with a graph of a straight line.

If we subtract the* x* squared from both
sides, we would end up with.
Is this a linear equation? Note how we have an *x *squared
as opposed to* x *to the one power.

It looks like we cannot write it in the form A*x* + B*y *= C because the *x* has to be to the one power, not squared. So **this is not a
linear
equation. **

**Step 1: Find three ordered pair
solutions.**

You do this by plugging in ANY three values for *x* and find their corresponding y values.

Yes, it can be ANY three values you want, 1, -3,
or even 10,000.
Remember there are an infinite number of solutions. As long as
you
find the corresponding *y *value that
goes with
each *x, *you have a solution.

To review ordered pair solutions go to **Tutorial
20: The Rectangular Coordinate System.**

**Step 2: Plot the points found
in step 1.**

Remember that each ordered pair corresponds to
only one point on the
graph.

The point lines up with both the* x* value
of the ordered pair (*x*-axis) and the *y *value
of the ordered pair (*y*-axis).

To review how to plot points on the graph go to **Tutorial
20: The Rectangular Coordinate System.**

**Step 3: Draw the graph.**

If you know it is a linear equation and your points don’t line up, then you either need to check your math in step 1 and/or that you plotted all the points found correctly.

I’m going to use a chart to organize my
information. A
chart keeps track of the *x* values that
you
are using and the corresponding *y* value
found when you used a particular *x* value.

If you do this step the same each time, then it will make it easier for you to remember how to do it.

I usually pick out three points when I know I’m dealing
with a line.
The three *x* values I’m going to use are
-1,
0, and 1. **(Note that you can pick ANY three x values that you
want. You do not have to use the values that I picked.) **You
want to keep it as simple as possible. The following is the chart
I ended up with after plugging in the values I mentioned for *x*.

I’m going to use a chart to organize my
information. A
chart keeps track of the *x* values that
you
are using and the corresponding *y* value
found when you used a particular *x* value.

If you do this step the same each time, then it will make it easier for you to remember how to do it.

I usually pick out three points when I know I’m dealing
with a line.
The three *x* values I’m going to use are
-1,
0, and 1. **(Note that you can pick ANY three x values that you
want. You do not have to use the values that I picked.) **You
want to keep it as simple as possible. The following is the chart
I ended up with after plugging in the values I mentioned for *x*.

** Practice Problems**

These are practice problems to help bring you to the
next level.
It will allow you to check and see if you have an understanding of
these
types of problems. **Math works just like
anything
else, if you want to get good at it, then you need to practice
it.
Even the best athletes and musicians had help along the way and lots of
practice, practice, practice, to get good at their sport or instrument.**
In fact there is no such thing as too much practice.

To get the most out of these, **you should work the
problem out on
your own and then check your answer by clicking on the link for the
answer/discussion
for that problem**. At the link you will find the answer
as well as any steps that went into finding that answer.

Practice Problems 1a - 1b:Determine whether the equation is linear or not.

Practice Problems 2a - 2b:Graph the linear equation.

2a. *y* = 2*x* - 1

(answer/discussion
to 2a

** Need Extra Help on these Topics?**

**The following is a webpage
that can assist
you in the topics that were covered on this page: **

**http://www.purplemath.com/modules/graphlin.htm**

This webpage helps you with graphing linear equations.

**Go to Get
Help Outside the
Classroom found in Tutorial 1: How to Succeed in a Math Class for
some
more suggestions.**

Last revised on July 29, 2011 by Kim Seward.

All contents copyright (C) 2001 - 2011, WTAMU and Kim Seward. All rights reserved.