Question 582392
In general, if the line is {{{ y = m[1]*x + b }}},
then the line perpendicular to it has a slope
{{{ m[2] = -( 1/(m[1]) ) }}}
given:
{{{ 8x - 9y + 2 = 0 }}}
{{{ 9y = 8x + 2 }}}
{{{ y = (8/9)*x + 2/9 }}}
Any line perpendicular to this one has slope 
{{{ m[2] =  -(1/(8/9)) }}}
{{{ m[2] = -(9/8) }}}
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given that the line passes through (-7,-9 )
Now use the point-slope formula:
{{{ ( y - (-9) ) / ( x - (-7) ) = -(9/8) }}}
{{{ ( y + 9 ) / ( x + 7 ) = -(9/8) }}}
Multiply both sides by {{{ 8*( x + 7 ) }}}
{{{ 8*( y + 9 ) = -9*( x + 7 ) }}}
{{{ 8y + 72 = -9x - 72 }}}
{{{ 9x + 8y + 144 = 0 }}}
Here's a plot of the 2 lines:
{{{ graph( 400, 400, -20, 20, -20, 20, (8/9)*x + 2/9, -(9/8)*x  - 18) }}}