Question 1061714
{{{ x[mid] = ( 1 - 5 )/2 }}}
{{{ x[mid] = -2 }}}
and
{{{ y[mid] = ( 2 + 12 )/2 }}}
{{{ y[mid] = 7 }}}
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The slope of the line segment is:
{{{ ( 12 - 2 ) / ( -5 - 1 ) = 10/(-6) }}}
{{{ 10/(-6) = -5/3 }}}
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The required line goes through ( -2, 7 )
and has slope = {{{ -5/3 }}}
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Use the point-slope formula
{{{ ( y - 7 ) / ( x -(-2)  ) = -5/3 }}}
{{{ y - 7 = (-5/3)*( x + 2 ) }}}
{{{ y - 7 = (1/3)*( -5x - 10 ) }}}
{{{ y = (-5/3)*x - 10/3 + 7 }}}
{{{ y = (-5/3)*x -10/3 + 21/3 }}}
{{{ y = (-5/3)*x + 11/3 }}}
{{{ m + b = -5/3 + 11/3 }}}
{{{ m + b = 2 }}} 
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check answer:
does the line go through ( -2,7 ) ?
{{{ y = (-5/3)*x + 11/3 }}}
{{{ 7 = (-5/3)*(-2) + 11/3 }}}
{{{ 21 = 10 + 11 }}}
{{{ 21 = 21 }}}
OK