**Learning Objectives**

After completing this tutorial, you should be able to:

- Find the slope given a graph or two points.
- Know the relationship between slopes of parallel lines.
- Know the relationship between slopes of perpendicular lines.

** Introduction**

This tutorial takes us a little deeper into linear
equations.
We will be looking at the slope of a line. We will also look at
the
relationship between the slopes of parallel lines as well as
perpendicular
lines. Let's see what you can do with slopes.

** Tutorial**

The slope of a line **measures the steepness of the
line.**

Most of you are probably familiar with associating slope
with "rise
over run".

**Run **means how far left or right you move
from point to point.
On the graph, that would mean a **change of x values**.

**Here are some visuals to help you with this
definition:**

**Positive slope:**

**Note that when a line has a positive slope it goes up
left to right.**

**Note that when a line has a negative slope it goes
down left to right.**

*slope* = 0

**Note that when a line is horizontal the slope is 0.**

*slope* = undefined

**Note that when the line is vertical the slope is
undefined.**

Given two points and

The subscripts just indicate that these are two
different points.
It doesn't matter which one you call point 1 and which one you call
point
2 as long as you are consistent throughout that problem.

Note that we use the letter *m* to represent
slope.

** Example
1**: Find the slope of the straight line that passes through
(-5,
2) and (4, -7).

***Simplify**

**The slope of the line is -1.**

***Simplify**

It is ok to have a 0 in the numerator. Remember
that 0 divided
by any non-zero number is 0.

**The slope of the line is 0.**

***Simplify**

Since we did not have a change in the *x* values, the denominator of our slope became 0. This means that we
have an **undefined slope.** If you were to graph the line,
it
would be a vertical line, as shown above.

**The slope of the line is undefined.**

In other words, the slopes of parallel lines are equal.

**Note that two lines are
parallel if there slopes
are equal and they have different y-intercepts.**

In other words, **perpendicular
slopes are negative
reciprocals of each other.**

** 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 - 1d:Find the slope of each line if it exists.

1b.

1c.

1d.

Practice Problems 2a - 2b:Find the slope of the straight line that passes through the given points.

2a. (3, 5) and (-1, -8)

(answer/discussion
to 2a)

2b. (4, 2) and (4, -2)

(answer/discussion to 2b)

(answer/discussion to 2b)

** 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/slope.htm**

This webpage helps you with slope.

**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 31, 2011 by Kim Seward.

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