The chart shows the cost of tuition at a certain state univesity. Model the data in the chart with a linear fuction ,using the point (1,10129) and (3,11400). Predict the cost of college tution in 2004-2005.
College Year,x | Estimated Tuition,y |
1997-1998,0 | $9587 |
1998-1999,1 | $10129 |
1999-2000,2 | $10727 |
2000-2001,3 | $11400 |
2001-2002,4 | $12125 |
What is the linear model for the data?
Y=
Please Help and thank you
We want the equation of a line that passes through (1, 10129) , and (3, 11400) .
slope = (change in y's) / (change in x's)
slope = (10129 - 11400) / (1 - 3)
slope = (-1271) / (-2)
slope = 635.5
So, the equation of this line is
(y - 10129) = 635.5(x - 1)
y - 10129 = 635.5x - 635.5
y = 635.5x - 635.5 + 10129
y = 635.5x + 9493.5
To predict the cost of tuition in 2004-2005, we want to know what y equals when x matches the year 2004 - 2005.
The x value for the year 2001 - 2002 is 4
The x value for the year 2002 - 2003 is 5
The x value for the year 2003 - 2004 is 6
The x value for the year 2004 - 2005 is 7
So..we want to know what y equals when x equals 7.
Plug in 7 for x and solve for y.
y = 635.5(7) + 9493.5
y = 4448.5 + 9493.5
y = 13942
So, our line predicts the cost of tuition will be $13,942 in the school year 2004 - 2005.
*edit*
Here is a graph of the line with all the points on it: