Question 530828
What is the equation of the line passing through
(0,6) and (2,1) ?
the point-slope formula says:
( change in y ) / ( change in x ) = ( change in y ) / ( change in x )
Suppose I call the 2 given points {{{ P[1] }}}, and {{{ P[2] }}}
{{{ P[1] }}} = (x1 , y1)
{{{ P[2] }}} = (x2 , y2)
Change in y = y2 - y1
Change in x = x2 - x1
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The formula uses the concept that any point (x,y) is also
OK to use, so I can say
( change in y ) / ( change in x ) = ( y - y1 ) / ( x - x1 )
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Putting these ideas together,
( y - y1 ) / ( x - x1 ) = ( y2 - y1 ) / ( x2 - x1 )
Now you just have to substitute the actual numbers:
(x1,y1) = (0,6)
(x2,y2) = (2,1)
{{{ ( y - 6 ) / ( x - 0 ) = ( 1 - 6 ) / (  2 - 0 ) }}}
{{{ ( y - 6 ) / x = -5/2 }}}
{{{ y - 6 = (-5/2)*x }}}
{{{ y = (-5/2)*x + 6 }}}
check answer:
(2,1)
{{{ 1 = (-5/2)*2 + 6 }}}
{{{ 1 = -5 + 6 }}}
{{{ 1 = 1 }}}
OK