Question 570920
Use the point-slope formula
{{{ ( y -(-3) ) / ( x -(-2) ) = ( -9 -(-3) ) / ( -7 -(-2) ) }}}
{{{ ( y + 3 ) / ( x + 2 ) = ( -9 + 3 ) / ( -7 + 2 ) }}}
{{{ ( y + 3 ) / ( x + 2 ) = (-6) / (-5) }}}
{{{ ( y + 3 ) / ( x + 2 ) = 6/5 }}}
Multiply both sides by {{{ 5*( x + 2 ) }}}
{{{ 5*( y + 3 ) = 6*( x + 2 ) }}}
{{{ 5y + 15 = 6x + 12 }}}
{{{ 5y = 6x - 3 }}}
{{{ y = (6/5)*x - 3/5 }}}
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Does the line go through (-2,-3) and (-7,-9) ?
{{{ y = (6/5)*x - 3/5 }}}
{{{ -3 = (6/5)*(-2) - 3/5 }}}
{{{ -3 = -(12/5) - 3/5 }}}
{{{ -3 = -(15/5) }}}
{{{ -3 = -3 }}}
and
{{{ -9 = (6/5)*(-7) - 3/5 }}}
{{{ -9 = -(42/5) - 3/5 }}}
{{{ -9 = -(45/5) }}}
{{{ -9 = -9 }}}
OK