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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

 Jun 4, 2017
 #1
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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:

https://www.desmos.com/calculator/ppljdujg4v     smiley

 Jun 4, 2017
edited by hectictar  Jun 4, 2017

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