Question 1053974
First put the given equation into
the slope-intercept form
{{{ 6x - 3y = 8 }}}
{{{ -3y = -6x + 8 }}}
{{{ 3y = 6x - 8 }}}
{{{ y = 2x - 8/3 }}}
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Any line perpendicular to this line 
will have slope = {{{ m[2] = -1/m[1] }}}
where {{{ m[1] = 2 }}}
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{{{ m[2] = -1/2 }}}
given the point ( 7, 1 )
Now use the general point-slope formula
{{{ ( y - 1 ) / ( x - 7 ) = -1/2 }}}
{{{ y - 1 = (-1/2)*( x - 7 ) }}}
{{{ y = (-1/2)*( x - 7 ) + 2/2 }}}
{{{ y = (-1/2)*x + 7/2 + 2/2 }}}
{{{ y = (-1/2)*x + 9/2 }}}
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check:
Does it go through ( 7,1 ) ?
{{{ 1 = (-1/2)*7 + 9/2 }}}
{{{ 1 = -7/2 + 9/2 }}}
{{{ 2/2 = 2/2 }}}
OK
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Here's a plot of both lines:
{{{ graph( 400, 400, -12, 12, -12, 12, 2x - 8/3, (-1/2)*x + 9/2 ) }}}