Question 576066
If the given equation is put into the form
{{{ y = mx + b }}}
the slope of the other is {{{ -(1/m) }}}
{{{ 7x + 2y = 69 }}}
{{{ 2y = -7x + 69 }}}
{{{ y = -(7/2)*x + 69/2 }}}
{{{ -(1/m) = -(-2/7) }}}
{{{ -(1/m) = 2/7 }}}
So far I have
{{{ y = (2/7)x + b }}}
Now plug in (9,7) to find {{{b}}} 
{{{ 7 = (2/7)*9 + b }}}
{{{ b = 7 - 18/7 }}}
{{{ b = ( 49 - 18 )/7 }}}
{{{ b = 31/7 }}}
{{{ y = (2/7)*x + 31/7 }}}
Multiply both sides by {{{7}}}
{{{ 7y = 2x + 31 }}}
{{{ 2x - 7y = -31 }}} answer
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Here's a plot of the 2 equations:
 {{{ graph( 400, 400, -3, 12, -3, 12, (2/7)*x + 31/7, -(7/2)*x + 69/2 ) }}}