Question 419919
Both equations need to be in the form {{{ y = mx + b}}}
where {{{m}}} is the slope
{{{2x + 5y = 7}}}
{{{ 5y = -2x + 7}}}
{{{ y = (-2/5)*x + 7/5 }}}
Any line parallel to this one must have {{{m = -2/5}}}
--------------
(3,6) , (k,9)
The formula for line through 2 points is:
{{{ (y - 6) / (x - 3) = (9 - 6) / (k - 3) }}}
{{{  (y - 6) / (x - 3) = 3 / (k - 3) }}}
{{{ (y - 6)*(k - 3) = 3*(x - 3) }}}
{{{ k*y - 6k - 3y + 18 = 3x - 9 }}}
{{{ (k - 3)*y = 3x - 9 - 18 + 6k }}}
{{{ (k - 3)*y = 3x + 6k - 27 }}}
{{{ y = (3/(k - 3))*x + (6k - 27)/(k - 3) }}}
--------------
{{{ -2/5 = 3/(k - 3) }}}
{{{-2*(k - 3) = 15 }}}
{{{-2k + 6 = 15}}}
{{{-2k = 9}}}
{{{k = -9/2}}} answer
check answer:
{{{ y = (3/((-9/2) - 3))*x + (6*(-9/2) - 27)/((-9/2) - 3) }}}
{{{ y = (3/(-15/2))*x + (-27 - 27)/(-15/2) }}}
{{{ y = (-2/5)*x + (-27 - 27)/(-15/2) }}}
OK