Question

sabendo-se que f(1)=4 e f(3)=-6, determine a função f(x)=ax+b

Answer 1

Olá, Keylla.

Coeficiente angular m de f(x):

$m=\frac{f(3)-f(1)}{3-1}=\frac{-6-4}{2}=-5$

Coeficiente linear p de f(x):

$f(x)=mx+p=-5x+p\Rightarrow f(1)=-5\cdot1+p\Rightarrow \\\\4=-5+p\Rightarrow p=9$

$\therefore f(x)=mx+p\Rightarrow \boxed{f(x)=-5x+9}$