Question 688021
The slope of the line {{{ y = 3x - 4 }}} is {{{ 3 }}}
The slope of any line which is perpendicular to
this line is {{{ m[2] = -1/m[1] }}}
{{{ m[2] = -1/3 }}}
You can use the general point-slope formula
{{{ ( y -(-7) ) / ( x - 6 ) = -1/3 }}}
{{{ ( y + 7 ) / ( x - 6 ) = -1/3 }}}
{{{ 3*( y + 7 ) = -( x - 6 ) }}}
{{{ 3y + 21 = -x + 6 }}}
{{{ 3y = -x - 15 }}}
{{{ y = ( -1/3 )*x - 5 }}} 
The slope is -1/3
The y-intercept is -5 
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here's a plot of the 2 lines:
{{{ graph( 400, 400, -6, 6, -7, 4, 3x - 4, (-1/3)*x - 5 ) }}}