Question 973834
{{{ 4x + 3y = 6 }}}
{{{ 3y = -4x + 6 }}}
{{{ y = -(4/3)*x + 2 }}}
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Any line perpendicular to this line
will have slope = {{{ -1/m }}}
where {{{ m = -4/3 }}}
{{{ -1/m = 3/4 }}}
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The required line goes through ( -2,6 )
Now use point-slope formula
{{{ ( y - 6 ) / ( x -(-2) ) = 3/4 }}}
{{{ y - 6 = (3/4)*( x+2 ) }}}
{{{ 4y - 24 = 3x + 6 }}}
{{{ 4y = 3x + 30 }}}
{{{ y = (3/4)*x + 15/2 }}} answer
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check:
does it go through ( -2,6 )?
{{{ y = (3/4)*x + 15/2 }}} 
{{{ 6 = (3/4)*(-2) + 15/2 }}} 
{{{ 6 = -3/2 + 15/2 }}}
{{{ 6 = 12/2 }}}
{{{ 6 = 6 }}}
OK
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Here are plots of the 2 lines:
{{{ graph( 400, 400, -10, 10, -10, 10, (3/4)*x + 15/2 , -(4/3)*x + 2 ) }}}