Beginning Algebra
Tutorial 23:Slope
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".
Rise means how many units you move up or
down from point to
point. On the graph that would be a change in the y values.
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. 
Negative slope:
Note that when a line has a negative slope it goes
down left to right. 
Zero slope:
slope = 0
Note that when a line is horizontal the slope is 0. 
Undefined slope:
slope = undefined
Note that when the line is vertical the slope is
undefined. 
Slope Formula Given Two Points
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). 

*Plug in x and y values into slope formula
*Simplify

Make sure that you are careful
when one of
your values is negative and you have to subtract it as we did in line
2.
4  (5) is not the same as 4  5.
The slope of the line is 1. 
Example
2: Find the slope of the straight line that passes
through
(1, 1) and (5, 1). 

*Plug in x and y values into slope formula
*Simplify

It is ok to have a 0 in the numerator. Remember
that 0 divided
by any nonzero number is 0.
The slope of the line is 0. 
Example
3: Find the slope of the straight line that passes through
(3,
4) and (3, 6). 

*Plug in x and y values into slope formula
*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. 
Parallel Lines and Their Slopes

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 yintercepts.

Perpendicular Lines and Their
Slopes

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.
Need Extra Help on these Topics?
Last revised on July 31, 2011 by Kim Seward.
All contents copyright (C) 2001  2011, WTAMU and Kim Seward. All rights reserved.

