Question

considere a função de primeiro grau em que f(2) = 14 e f(-1) = -13. o valor de f(5) é?​

Answer 1

$Uma~funcao~do~1^o~grau~\acute{e}~dado~na~forma:~~\boxed{y=a.x+b}\\\\\\\\\underline{Para~~f(2)=14}:\\\\\\14~=~a.(2)+b\\\\\\\boxed{2a+b~=~14}\\\\\\\\\underline{Para~~f(-1)=-13}:\\\\\\-13~=~a.(-1)+b\\\\\\\boxed{-a+b~=\,-13}$

$\left\{\begin{array}{ccc}2a+b&=&14\\-a+b&=&-13\end{array}\right\\\\\\Utilizando~o~metodo~da~adicao~para~resolver~o~sistema.\\\\\\(2a+b)~-~(-a+b)~=~14~-~(-13)\\\\\\2a+b+a-b~=~14+13\\\\\\3a~=~27\\\\\\\boxed{a~=~9}\\\\\\-a+b~=\,-13\\\\\\-(9)+b~=\,-13\\\\\\b~=\,-13+9\\\\\\\boxed{b~=\,-4}$

$A~funcao~fica:~~y~=~9x-4\\\\\\\underline{Calculando~f(5)}:\\\\\\f(5)~=~9\,.\,(5)-4\\\\\\f(5)~=~45-4\\\\\\\boxed{f(5)~=~41}$