Question 1102497
{{{ 3y = 4 - 2x }}}
{{{ 3y = -2x + 4 }}}
{{{ y = (-2/3)*x + 4/3 }}}
This is in the form {{{ y = m*x + b }}}
where {{{ m }}} = slope, so
{{{ m = -2/3 }}}
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Any line perpendicular to this line will
have slope = {{{ -1/m }}}
{{{ -1/((-2/3)) = 3/2 }}}
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The unknown line passes through ( 3,7 )
You can use the general point-slope formula
{{{ ( y - 7 ) / ( x - 3 ) = 3/2 }}}
Multiply both sides by {{{ 2*( x - 3 ) }}}
{{{ 2*( y - 7 ) = 3*( x - 3 ) }}}
{{{ 2y - 14 = 3x - 9 }}}
{{{ 2y = 3x + 5 }}}
{{{ y = (3/2)*x + 5/2 }}}
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check the answer:
Does it go through ( 3,7 ) ?
{{{ 7 = (3/2)*3 + 5/2 }}}
{{{ 7 = 9/2 + 5/2 }}}
{{{ 7 = 14/2 }}}
{{{ 7 = 7 }}}
OK