Question

determine a função f(x) = ax+b, sabendo que f(1) = 5 e f(-3) = -7

Answer 1

          f(x) = ax + b

         f(1) = 5 = a(1) + b
                          a + b = 5    (1)
         f(-3) = - 7 = a(-3) + b
                        -3a + b = - 7  (2)
 
             Resolvendo sistema (1) (2)
                (1) x (- 1)
                    - a - b = - 5      (3)
               (3) + (2)
                              - 4a = - 7 - 5
                              - 4a = - 12
                                  a = - 12/- 4
                                                         a = 3
          a em (1)
                           3 + b = 5
                                 b = 5 - 3
                                                        b = 2

             A FUNÇÃO É
                f(x) = 3x + b

Answer 2

$\left \{ {{5=a.1+b--\ \textgreater \ 5=a+b . (3)--\ \textgreater \ 15=3a+3b} \atop {-7=a. (-3)+b--\ \textgreater \ -7=-3a+b}} \right. (+);8=4b--\ \textgreater \ b=\frac{8}{4} --\ \textgreater \ b=2;$ $5=a+b --\ \textgreater \ 5=a+2--\ \textgreater \ 5-2=a--\ \textgreater \ a=3;$ $f(x)=3x+2$