In this lesson we will introduce one of the most important
components of graphing linear equations...
the slope of a line.

Let's begin with a simple example which should help
you to understand this somewhat complex concept.
 

As you can clearly see from the two "hills" above, one of the
hills would be much more difficult to climb than the other.
The "hill" on the left has a much steeper "slope".

In mathematical language, the slope is defined
as the ratio of the change in vertical distance,
which is called the "rise",
to the change in horizontal distance,
which we call the "run".

Let's look at the Hard Hill first.....
As you can see
 the vertical distance = 30
the horizontal distance = 60
Therefore the slope of this hill can be expressed as:
30/60 or 1/2
Now let's look at the Easy Hill...
the vertical distance = 15
the horizontal distance = 60
Therefore the slope of this hill can be expressed as:
15/60 or 1/4
   As you can see the slopes are not the same...
we can also make the assumption that
the smaller the ratio (or fraction)
the less "steep" is the slope.

Now let's look at how this works on the coordinate plane:

As you can see from this example,
the rise of this line is 3, and the run is also 3
That makes the slope of this line (rise/run) = 3/3 or 1

I mentioned that this is a fairly complex concept...
See what I mean!!!
On the next page we will learn what happens to the
slope as the line changes direction.
Click below to continue our lesson.

To continue our exploration of slope please...

CLICK HERE