Question 490189
{{{ 2y = kx + h }}}
passes through the points
(-3,6) and (1,11)
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Plug in (x,y) = (-3,6)
{{{ 2*6 = k*(-3) + h }}}
(1) {{{ 12 = -3k + h }}}
and
(x,y) = (1,11)
{{{ 2*11 = k*1 + h }}}
(2) {{{ 22 = k + h }}}
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Rewrite both equations in reverse order
(1) {{{ h - 3k = 12 }}}
(2) {{{ h + k = 22 }}}
Subtract (1) from (2)
(2) {{{ h + k = 22 }}}
(1) {{{ -h + 3k = -12 }}}
{{{ 4k = 10 }}}
{{{ k = 5/2 }}}
and, since
{{{ h + k = 22 }}}
{{{ h + 5/2 = 22 }}}
{{{ 2h + 5 = 44 }}}
{{{ 2h = 39 }}}
{{{ h = 39/2 }}}
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check:
Does the equation pass through the points?
{{{ 2y = kx + h }}}
{{{ 2y = (5/2)*x + 39/2 }}}
{{{ y = (5/4)*x + 39/4 }}}
(-3,6)
{{{ 6 = (5/4)*(-3) + 39/4 }}}
{{{ 6 = -15/4 +39/4 }}}
{{{ 6 = 24/4 }}}
{{{ 6 = 6 }}}
OK
(1,11)
{{{ y = (5/4)*x + 39/4 }}}
{{{ 11 = (5/4)*1 + 39/4 }}}
{{{ 11 = 44/4 }}}
{{{ 11 = 11 }}}
OK