The Pumpkin Problem
There is a County Fair in Topsfield, Massachusetts where they hold a competition for who has the largest pumpkin, in weight. All trying to get the main prize....a blue ribbon. Yes, a very exciting award, but it's better than nothing. So each year, a winner is selected. All of the heaviest pumpkins have been recorded from the 1984 fair till the 1993 fair. My job was to predict, using awesome Algebra, what the weight of the winning pumpkin in the year 2004. Was it tough? Maybe it was...

Process and Solution
How did I get started on this adventure to get some sort of prediction of the 2004 winner?  Well, firstly I created a scatter plot with all the previous years winners and plotted those points. Pretty easy to do. Then came a thing called the Line of Regression, which is a line that you choose that goes through or more points on a graph to get a some what more accrurate assumption. Now, with two points off of the Line of Regression, I used them to find a slope for my Line of Regression.  I chose the points (1984, 433) and (1992, 718). To find the slope, I used this formula:
Y² - Y¹
X² - X¹
Plugging those numbers correctly into the right places, I came up with a slop of 285/8, which roughly  comes out to be 35.6. That would be the slope of my sort of developed equation. So far, I would have this:

y = 35.6x+b

Now, I would have to find a Y-Intercept for my equation. But a Y-Intercept in this type of problem isn't really relevant because we are dealing with real life matters. Still, I would have to find my "really-cool-but-not-really-cool" Y-Intercept. I knew it was going to be huge. So, to get my Y-Intercept, I plugged the points (1984, 433) into the above equation, which would look like this:

433 = 35.6(1984)+b

Then followed by the math:

433 = 70630.4+b
(subtract 70630.4 from both sides)
-70197.4=b

Woooooo! There's what I am looking for. 

y = 35.6x - 70197.4

Now I have a complete equation and can now find out results. By plugging in (2004,y) into that equation, I finally get an answer:

y = 35.6(2004) - 70197.4
y = 71342.4 - 70197.4
y = 1145

YES!! My math has come up for a prediction of the weight of the pumpkin in the 2004 Topsfield, Massachusetts County Fair. At a whopping 1145 pounds, this weight should be around how heavy the 2004 winning pumpkin should weigh. Right?

(All of my actual written work should be on the other picture file, which I scanned. All of it should be there to varify all of this)  :-)

Evaluation
After doing a previous problem like this, with two lines actually, this was pretty simple to accomplish. The other one I did before this was a little "tougher" than this because I would have to find slopes of two lines, and then I would have to find out at which points these two lines would meet at.  The math I used was actually two equations I think. The Point-Slope and the Y-Intercept equations. Very simple to use if you know how to use them correctly. Both of these equations REALLY helped out into finding a predtiction in this problem because you actually sort of need to use them to find one any ways.