Apply Linear Equation in two Variables

I'm doing Example 8 from page 38 Chapter P.4 and it asks me to find the Linear Model for Americans' Personal incomes.

On question (A) i use the point that were given (x1, y1), (x2, y2) ..(1998, 7.4), (1999, 7.8) I used the formula to find for the slope which is (y2-y1 over x2-x1) Then after i got the slope i find the y-intercept by pluging the slope and point (1998, 7.4) into the equation of the slope-intercept form. Then i got this equation (y=0.4x-791.8) in the form of (y=mx+b)

Then, on (B) i just plug (2001) in to the equation to find the income of American in the year of 2001.

On (C) , it's basically the same as (b) but in a different year. I used the year of 2007 on that one.

(D) Is where a graph is shown from 1998-2006 (The American Income)

(E) Ask me that what may have happened that from 2000-2007 that can effect the income. I said that WAR can dicrease the American Income because it causes loss of jobs as well as homeless.

Graphing Functions

1. The original graph i used is the one in color "Black" . It's original funtion is y= [x] (y is equal to the absolute value of X. That is what you get if you were to graph it.

2. I wanted to verticle translate this original graph so what i do is i move it down vertically 4 units. This vertical translation gave us the new funtion y=[x] -4 which is shown is the red graph above.

3. Then, Said i want make a horizontal translation it's very similar to verticle translation but this time you would have to go horizontally across the x-intercept instead. In blue graph above i horizontal translate it 8 units to the left which gave me the new function of y= [x-8]

4. Now if you want to recflect this across the x-axis you would have to do the reflection by flipping the graph over (shown in purple graph above). This new funtion is y= -[x] (where negative is on the outside)

5. After that, you can also combine both the vertical "and" horizontal translation. This means that you are moving the graph in 2 directions, "vertically" and "horizontally". In this funtion i move the graph 8 units to the right" horizontally" and 4 units down "vertically". It's shown in the green graph above.

6. Finally, WHAT'S Awesome! is that you can actually combine the whole thing by creating this tranformation just by putting together the ( verical (4 down) +horizonal (8 right) translation and our reflection across the x-axis) When you put them together your result will be the same as in my green graph. This new funtion gives us y= -[x-8]-4

About ME

About "Ravuth -__-"
Background:
Bancroft Middle School
Oakland High school ^^ 2012

What I want to be:
-Anything really... which involves space :D.. Want to sit near a telescope someday..

Interests:
-Fishing! never caught a big fish before unfortunately...
-Computer!! it's my life XD
-Volleyball i like how it requires speed, power, and focus...