Question 1129600
{{{ x - 5y = 6 }}}
{{{ 5y = x - 6 }}}
{{{ y = (1/5)*x - 6/5 }}}
Any line parallel to this line will have
slope = {{{ m = 1/5 }}}
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( -3,5 )
Use the general point-slope formula
{{{ ( y - 5 ) / ( x -(-3) ) = 1/5 }}}
{{{ y - 5 = (1/5)*( x + 3 ) }}}
{{{ 5y - 25 = x + 3 }}}
{{{ x - 5y = -28 }}}
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check:
Does it go through ( -3,5 )
{{{ -3 - 5*5 = -28 }}}
{{{ -3 - 25 = -28 }}}
{{{ -28 = -28 }}}
OK
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{{{ 3x - y = 4 }}}
{{{ y = 3x - 4 }}}
Any line perpendicular to this line will have
slope {{{ m = -1/3 }}} because
{{{ m[1] = -1/m }}}
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( -4,7 )
{{{ ( y - 7 ) / ( x -(-4) ) = -1/3 }}}
Multiply both sides by {{{ 3*( x + 4 ) }}}
{{{ 3*( y - 7 ) = -( x + 4 ) }}}
{{{ 3y - 21 = -x - 4 }}}
{{{ x + 3y = 17 }}}
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check:
(-4,7)
{{{ -4 + 3*7 = 17 }}}
{{{ -4 + 21 = 17 }}}
{{{ 17 = 17 }}}
OK