Question 1055390
Plot {{{ t }}} = time in months on the horizontal axis
Plot {{{ E }}} = the number of employees at the end
of {{{ t }}} months on the vertical axis
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You are given 2 points on a straight line:
(  t,E ) = ( 1, 2 ) and ( 6, 10 )
Use the general point-slope formula
{{{ ( E - 2 ) / ( t - 1 ) = ( 10 - 2 ) / ( 6 - 1 ) }}}
{{{ ( E - 2 ) / ( t - 1 )  = 8/5 }}}
Multiply both sides by {{{ 5*( t-1 ) }}}
{{{ 5*( E - 2 ) = 8*( t - 1 ) }}}
{{{ 5E - 10 = 8t - 8 }}}
{{{ 5E = 8t + 2 }}}
{{{ E = (8/5)*t + 2/5 }}}
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check answer:
Does it go through ( 1,2 ) ?
{{{ E = (8/5)*t + 2/5 }}}
{{{ 2 = (8/5)*1 + 2/5 }}}
{{{ 2 = 8/5 + 2/5 }}}
{{{ 2 = 2 }}}
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Does it go through ( 6, 10 )
{{{ E = (8/5)*t + 2/5 }}}
{{{ 10 = (8/5)*6 + 2/5 }}}
{{{ 10 = 48/5 + 2/5 }}}
{{{ 10 = 50/5 }}}
{{{ 10 = 10 }}}
OK