Tuesday, October 5, 2010

Ch. P - Applying Linear Equation in Two variables

For this project, I chose to do problem #8 on page 38. The problem required:
(a) Write a linear equation for Americans' income in y in terms of the year x using the points (1998, 7.4) and (1999, 7.8).
First - I used m= y2 - y1/ x2-x1 and substituted my points in to find the slope.
Second - I used slope-intercept form which is y=mx + b to find the linear equation so I can get the y-intercept.
Third - I get my equation which is y=0.4x - 791.8
(b) Use the equation in (a) to estimate Americans' income in 2001.
First - Find y when x=2001 in slope-intercept form. Put 2001 in for the x value in the equation from (a).
Second - The answer will be 8.6 trillion which is only 0.1 off from 8.7 trillion.
(c) Use the equation in (a) to predict Americans' income in 2008.
First - Use the same steps as (b), but instead of 2001, use 2008.
Second - The answer will be 10.4 trillion.
(d) Superimpose a graph of the linear equation in (a) on a scatter plot of the data.
First - I used my graphing calculator to make my scatter plot by plugging in all the points.
Second - I pressed the [Y=] button and plugged in my equation from (a).
Third - You will see a line running through the first 2 points in your scatter plot and touching the other points.
By finding the slope and using the slope-intercept form to write a linear equation, I am able to estimate and predict Americans' income for any year that I want.

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