Blog Post #4 - Lesson on Slope

Hello class, my name is Professor Hutkoff substituting for your beloved Professor LIttle who is out today - and I will be teaching you all about the concept of slope.

Introduction
-First off, what is a slope?

Slope is the change in Y divided by the change in X, a good way to think about it is slope equals the rise over the run of a line on a graph.

-How does one find this "slope" that you speak of?

Slope can be calculated by the formula      with "m" representing the slope, so all you would need to find the slope would be two points for the x's and y's.

Slope can also be found just by simply looking at your graph and counting the number of units for the rise and for the run (pictured below).




-Now that I have this crazy slope thing, what can I do with it?

The slope is a part of a very important equation in Algebra called the y-intercept form which is the formula of a linear equation, y=mx+b, where again, "m" is equal to the slope. Slope is vital to this formula and along with "b," which is representative of the y-intercept in the equation, one is able to successfully graph a line by using the y-intercept form.

Examples

1.) You are given the points (4,1) and (7,5). Find the slope.
Using the slope equation mentioned previously:
You would take 5 and subtract 1 equalling 4
And you would take 7 and subtract 4 equalling 3
With your end result being 4/3 for the slope

2.) For a real world scenario of how one could use slope, we'll examine the example of measuring the steepness of a roof on a building. Say you are charged with conducting repairs on the roof of a building but first you must find the slope of the roof so that you can properly repair it.
You would use a measuring device (i.e. a ruler) to find the rise and run of the roof.
If your rise was 8ft and the span of the roof was 30ft (assuming the roof is evenly divided down the middle of the building), your run would have to be 15ft.
Rise = 8 
Run = 15           therefore 8/15 would be the sloop.


And that concludes my lesson for the day class, hopefully you are leaving today satisfied with your newfound knowledge of this amazing and applicable concept of slope. Don't forget to turn in your exit slips before you leave!

Sources:
http://www.mathwarehouse.com/algebra/linear_equation/images/slope_given_2points/slope-of-a-line-graph.gif
http://math.about.com/od/algebra1help/a/Slope_Line_Graph.htm
http://www.roofhelp.com/images/roofhelp/slope.gif