SOLUTION: Hi, again I need some help this paper is due tomorrow hope someone has time to help. I need to create a function using this information. year Median Home Cost 1989 $93,100 19

Algebra ->  Functions -> SOLUTION: Hi, again I need some help this paper is due tomorrow hope someone has time to help. I need to create a function using this information. year Median Home Cost 1989 $93,100 19      Log On


   

Question 132398: Hi, again I need some help this paper is due tomorrow hope someone has time to help. I need to create a function using this information.
year Median Home Cost
1989 $93,100
1990 $97,500
1991 $99,700
1992 $100,900
1993 $106,100
Using the data from 1989 and 1992 determine the values for M and B and then create a linear functionf(x) = mx + b.
m_____; B_____ f(x) = __________.
Thanks for your help.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you need to use all the data that is given, then use your calculator to calculate the linear regression.

If you just want to find the line through the points (1989, 93100) and (1992,100900) then let's make the year 1989 as x=0 (ie we're starting at the year 1989)

So the two points then become (0, 93100) and (3,100900). Notice how 1992 is 3 years from 1989. So at 1992, we have x=3


Now let's find the equation of the line through the points (0, 93100) and (3,100900)


First lets find the slope through the points (0,93100) and (3,100900)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (0,93100) and is the second point (3,100900))

m=%28100900-93100%29%2F%283-0%29 Plug in y%5B2%5D=100900,y%5B1%5D=93100,x%5B2%5D=3,x%5B1%5D=0 (these are the coordinates of given points)

m=+7800%2F3 Subtract the terms in the numerator 100900-93100 to get 7800. Subtract the terms in the denominator 3-0 to get 3


m=2600 Reduce

So the slope is
m=2600

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-93100=%282600%29%28x-0%29 Plug in m=2600, x%5B1%5D=0, and y%5B1%5D=93100 (these values are given)


y-93100=2600x%2B%282600%29%280%29 Distribute 2600

y-93100=2600x%2B0 Multiply 2600 and 0 to get 0

y=2600x%2B0%2B93100 Add 93100 to both sides to isolate y

y=2600x%2B93100 Combine like terms 0 and 93100 to get 93100
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Answer:


So the equation of the line which goes through the points (0,93100) and (3,100900) is:
y=2600x%2B93100 (or in function notation is f%28x%29=2600x%2B93100 )

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=2600 and the y-intercept is b=93100