Question 132398
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=(y[2]-y[1])/(x[2]-x[1])}}} Start with the slope formula (note: *[Tex \Large \left(x_{1},y_{1}\right)] is the first point ({{{0}}},{{{93100}}}) and  *[Tex \Large \left(x_{2},y_{2}\right)] is the second point ({{{3}}},{{{100900}}}))


{{{m=(100900-93100)/(3-0)}}} Plug in {{{y[2]=100900}}},{{{y[1]=93100}}},{{{x[2]=3}}},{{{x[1]=0}}}  (these are the coordinates of given points)


{{{m= 7800/3}}} 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[1]=m(x-x[1])}}} where {{{m}}} is the slope, and *[Tex \Large \left(\textrm{x_{1},y_{1}}\right)] is one of the given points


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


{{{y-93100=(2600)(x-0)}}} Plug in {{{m=2600}}}, {{{x[1]=0}}}, and {{{y[1]=93100}}} (these values are given)



{{{y-93100=2600x+(2600)(0)}}} Distribute {{{2600}}}


{{{y-93100=2600x+0}}} Multiply {{{2600}}} and {{{0}}} to get {{{0}}}


{{{y=2600x+0+93100}}} Add {{{93100}}} to  both sides to isolate y


{{{y=2600x+93100}}} 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+93100}}}  (or in function notation is {{{f(x)=2600x+93100}}} )


The equation is now in {{{y=mx+b}}} form (which is slope-intercept form) where the slope is {{{m=2600}}} and the y-intercept is {{{b=93100}}}