Question 1097346
You are given 2 straight lines and the slopes of
those lines.
Let {{{ M }}} = the population of Morganville for
any given year
Let {{{ C }}} = population of Crowley for any given year
Ley {{{ y }}} = the number of the year starting with
2010 is {{{ y = 0 }}}
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For Morganville in 2010, you are given the point
( 0, 3750 )
The slope for Morganville is {{{ 270 }}} people/yr
{{{ M = 270y + b }}} 
{{{ 3750 = 270*0 + b }}}
{{{ b = 3750 }}}
The equation is 
{{{ M = 270y + 3750 }}}
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For Crowley, the point is:
( 0, 3000 )
The slope is {{{ 120 }}} people/yr
{{{ C = 120y + b }}}
{{{ 3000 = 120*0 + b  }}}
{{{ b = 3000 }}}
The equation is:
{{{ C = 120y + 3000 }}}
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Find {{{ y }}} when {{{ M= C }}}
{{{ 270y + 3750 = 120y + 3000 }}}
{{{ 150y = -750 }}}
{{{ y = -5 }}}
Since 2010 means {{{ y=0 }}} then
2010 - 5= 2005 
In 2005 the populations were the same
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check:
Here are the plots of the lines:
{{{ graph( 400,400, -10, 10, -1000, 6000, 270x + 3750, 120x + 3000 ) }}}