Question 726844
So I don't have to use fractions, 
I'll say {{{ a = 1/12 }}}, so
{{{ 1/4 = 3a }}}
{{{ -1/4 = -3a }}}
{{{ -1/3 = -4a }}}
-----------------
( 3a,  -4a ), ( -3a, -3 )
Use point slope formula
{{{ ( y -(-3) ) / ( x -(-3a) ) = ( -4a -(-3) ) / ( 3a -(-3a) ) }}}
{{{ ( y  + 3 ) / ( x  + 3a ) = ( -4a + 3 ) / ( 3a  + 3a ) }}}
{{{ ( y  + 3 ) / ( x  + 3a ) = ( -4a + 3 ) / 6a }}}
Multiply both sides by {{{ 6a*( x + 3a ) }}}
{{{ 6a*( y + 3 ) = ( -4a + 3 )*( x + 3a ) }}}
{{{ 6a*y + 18a = -4a*x + 3x -12*a^2 + 9a }}}
{{{ 6a*y = ( 3 - 4a )*x - 12*a^2 - 9a }}}
Substitute {{{ a = 1/12 }}}
{{{ (1/2)*y = ( 3 - 1/3 )*x - 12*(1/144) - 9*(1/12) }}}
{{{ (1/2)*y = ( 8/3 )*x - 1/12 - 9/12 }}}
Multiply both sides by {{{ 12 }}}
{{{ 6y = 32x - 10 }}}
{{{ y = ( 16/3 )*x - 5/3 }}}
check:
does it go through ( 1/4, -1/3 ) ?
{{{ -1/3 = ( 16/3 )*(1/4) - 5/3 }}}
{{{ -1/3 = 4/3 - 5/3 }}}
{{{ -1/3 = -1/3 }}}
OK -you can check the other point