Question 973859
{{{ x[M]= ( 6 +(-2) ) / 2 }}}
{{{ x[M] = 4/2 }}}
{{{ x[M] = 2 }}}
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{{{ y[M] = ( 11 + 3 ) / 2 }}}
{{{ y[M] = 14/2 }}}
{{{ y[M] = 7 }}}
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The midpoint of the line LN is at ( 2,7 )
Now find slope of line LN
{{{ m = ( 11 - 3 ) / ( 6 -(-2) ) }}}
{{{ m = 8 / 8 }}}
{{{ m = 1 }}}
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Any line perpendicular to LN will have
slope = {{{ -1/m = - 1/1 }}}
slope = {{{ -1 }}}
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Now use general point-slope formula:
{{{ ( y - 7 ) / ( x - 2 ) = -1 }}}
{{{ y - 7 = -1*( x - 2 ) }}}
{{{ y - 7 = -x + 2 }}}
{{{ y = -x + 9 }}} answer
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check: 
does it go through ( 2,7 )?
{{{ 7 = -2 + 9 }}}
{{{ 7 = 7 }}}
OK