Question 717112
The slope of the line {{{ y = 2x - 4 }}}
is {{{ m[1] = 2 }}}
Any line which is perpendicular to the line
{{{ y = 2x - 4 }}}  will have slope
{{{ m[2] = -1/m[1] }}}
{{{ m[2] = -1/2 }}}
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(-6,-2)
Use the general point-slope formula
{{{ ( y -(-2) ) / ( x -(-6) ) = -1/2 }}}
{{{ ( y + 2 ) / ( x + 6 ) = -1/2 }}}
Multiply both sides by {{{ 2*( x + 6 ) }}}
{{{ 2*( y + 2 ) = -( x + 6 ) }}}
{{{ 2y + 4 = -x - 6 }}}
{{{ 2y = -x - 10 }}}
{{{ y = -(1/2)*x - 5 }}}
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check answer:
Does it go through (-6,-2) ?
{{{ -2 = -(1/2)*(-6) - 5 }}}
{{{ -2 = 3 - 5 }}}
{{{ -2 = -2 }}}
OK
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Here's a plot of the 2 lines:
{{{ graph( 400, 400, -6, 6, -10, 2, 2x - 4, -(1/2)*x - 5 ) }}}