Question 1153736
 In 1986, {{{523000}}} people worked in the air transportation industry. 
In 2002, the number was {{{485000}}}.


(a) Find a linear equation giving the number of employees in the air transportation industry in terms of​ {{{x}}}, the number of years since {{{1986}}}.

{{{x=6}}} in {{{1986}}}

let the number of employees be {{{y}}} divided by {{{1000}}} to make it simplier


linear equation is: {{{y=mx+b}}}


given two points:
({{{6}}},{{{523}}})

({{{16}}},{{{485}}})



use points to find a slope {{{m}}}

{{{m=(y[2]-y[1])/(x[2]-x[1])}}}

{{{m=(485-523)/(16-6)}}}

{{{m=(-38)/10}}}

{{{m=-3.8}}}



{{{y=-3.8x+b}}}


use one point to find {{{b}}}


{{{523=-3.8*6+b}}}

{{{523=-22.8+b}}}

{{{b=523+22.8}}}

{{{b=545.80}}}



so, equation is 

{{{y=-3.8x+545.8}}}



(b) Assuming the equation remains valid in the​ future, in what year will there be {{{430000}}} employees of the air transportation​ industry?


{{{y=430}}}

{{{430=-3.8x+545.8}}}

{{{3.8x=545.8-430}}}

{{{3.8x=115.8}}}

{{{x=115.8/3.8}}}

{{{x=30.4737}}}


we started with year {{{1986}}}, so add {{{30.4737}}}years
a year will be in {{{1986+30.4737=2016.4737}}} 

middle of {{{2016}}}



check:
so, now {{{x=30.4737}}}

{{{430=-3.8*30.4737+545.8}}}
{{{430=-115.8+545.8}}}
{{{430=483}}}