Question 647577
There are no special problems. Just use 
standard methods to add and subtract
fractions
given:
(1/3,-1/2) and (-1/3, -3) 
Use the general point-slope formula
{{{ (( y - (-1/2) )) / (( x - 1/3 )) = (( -3 - (-1/2) )) / (( -1/3 - 1/3 )) }}}
{{{ (( y + 1/2 )) / (( x - 1/3 )) = (( -3 + 1/2 )) / (( -2/3 )) }}}
Multiply both sides by {{{ (-2/3 )*( x - 1/3 ) }}}
{{{ (-2/3) *( y + 1/2 ) = ( -6/2 + 1/2 )*( x - 1/3 ) }}}
{{{ (-2/3)*y - 1/3 = (-5/2)*( x - 1/3 ) }}}
{{{ (-2/3)*y - 1/3 = (-5/2)*x  + 5/6  }}}
{{{ (5/2)*x - (2/3)*y = 5/6 + 1/3 }}}
Multiply both sides by {{{ 6 }}}
{{{ 15x - 4y = 5 + 2 }}}
{{{ 15x - 4y = 7 }}}
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check answer 
Does it go through the given points?
( 1/3, -1/2 )
{{{ 15x - 4y = 7 }}}
{{{ 15*(1/3) - 4*(-1/2) = 7 }}} 
{{{ 5 + 2 = 7 }}}
{{{ 7 = 7 }}}
OK
( -1/3,-3 )
{{{ 15*(-1/3) - 4*(-3) = 7 }}}
{{{ -5 + 12 = 7 }}}
{{{ 7 = 7 }}}
OK
Hard to keep straight, but it works