Question 1036485
Let the general form of the linear
equation be:
{{{ f(x) = a*x + b }}}
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given:
(1) {{{ f(2) = a*2 + b }}}
(2) {{{ f(6) = a*6 + b }}}
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Also given:
{{{ f(2) = 3 }}}
(1) {{{ 3 = a*2 + b }}}
and
{{{ f(6) = 4 }}}
(2) {{{ 4 = a*6 + b }}}
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Rewrite (1) and (2)
(1) {{{ 2a + b = 3 }}}
(2) {{{ 6a + b = 4 }}}
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subtract (1) from (2)
(2) {{{ 6a + b = 4 }}}
(1) {{{ -2a - b = -3 }}}
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{{{ 4a = 1 }}}
{{{ a = 1/4 }}}
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and
(1) {{{ 2*(1/4) + b = 3 }}}
(1) {{{ 1/2 + b = 3 }}}
(1) {{{ 1 + 2b = 6 }}}
(1) {{{ 2b = 5 }}}
(1) {{{ b = 5/2 }}}
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So, the linear equation is:
{{{ f(x) = (1/4)*x + 5/2 }}}
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check:
{{{ f(2) = 3 }}}
{{{ x = 2 }}}
{{{ (1/4)*2 + 5/2 = 3 }}}
{{{ 1/2 + 5/2 = 3 }}}
{{{ 6/2 = 3 }}}
{{{ 3 = 3 }}}
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{{{ f(6) = 4 }}}
{{{ x = 6 }}}
{{{ (1/4)*6 + 5/2 = 4 }}}
{{{ 3/2 + 5/2 = 4 }}}
{{{ 8/2 = 4 }}}
{{{ 4 = 4 }}}
OK