Question 983884
{{{ 4x - 3y = 10 }}}
{{{ 3y = 4x - 10 }}}
{{{ y = (4/3)*x - 10/3 }}}
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The line is now in the form:
{{{ y = m*x + b }}} where
{{{ m }}} = slope
For this line, {{{ m = 4/3 }}}
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ANY line perpendicular to this line
will have slope = 
{{{ m[1] = -1/m }}}
{{{ m[1] = -1/(4/3) }}}
{{{ m[1] = -3/4 }}}
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The required line goes through: (8,-3)
You can use the point-slope formula:
{{{ ( y - (-3) ) / ( x - 8 ) = -3/4 }}}
{{{ y + 3 = ( -3/4 )*( x - 8 ) }}}
{{{ y + 3 = (-3/4)*x + 6 }}}
{{{ y = (-3/4)*x + 3 }}} answer
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check:
Does it go through (8,-3) ?
{{{ y = (-3/4)*x + 3 }}} 
{{{ -3 = (-3/4)*8 + 3 }}} 
{{{ -3 = -6 + 3 }}}
{{{ -3 = -3 }}}
OK
Here are the plots of the lines:
{{{ graph( 400, 400, -10, 10, -10, 10, (4/3)*x - 10/3, (-3/4)*x + 3 ) }}}
Hope this helps