Question 1118390
{{{ 4x - 3y = 10 }}}
{{{ 3y = 4x - 10 }}}
{{{ y = (4/3)*x - 10/3 }}}
If the slope of this line is {{{ m[1] = 4/3 }}},
then any line perpendicular to it has
slope  {{{m[2] = -1/m[1] = -3/4 }}}
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The unknown line looks like:
{{{ y = m[2]*x + b }}}
Plug in the point ( 8, -3 )
{{{ -3 = ( -3/4 )*8 + b }}}
{{{ -3 = -6 + b }}}
{{{ b = 3 }}}
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The equation of the unknown line is:
{{{ y = (-3/4)*x + 3 }}}
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check:
Plug in ( 8, -3 )
{{{ -3 = (-3/4)*8 + 3 }}}
{{{ -3 = -6 + 3 }}}
{{{ -3 = -3 }}}
OK