Question

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Encontre a função que passa pelos pontos (-1,2) e (2,8)

Answer 1

Dados: 

Pares ordenados: (-1,2) e (2,8)
F(x) = ?

Cálculo: 

$\displaystyle \mathsf{(-1,2)}\\ \\ \displaystyle \mathsf{y = ax + b}\\ \\ \displaystyle \mathsf{x = -1; y = 2}\\ \\ \displaystyle \mathsf{2 = a.(-1) + b}\\ \displaystyle \mathsf{-a + b = 2}$

$\displaystyle \mathsf{(2,8)}\\ \\ \displaystyle \mathsf{y = ax + b}\\ \\ \displaystyle \mathsf{x = 2; y = 8}\\ \\ \displaystyle \mathsf{8 = a.(2) + b}\\ \displaystyle \mathsf{2a + b = 8}$

$\displaystyle \mathsf{ \left \{ {{-a + b = 2} \atop {2a + b = 8}} \right. }\\ \\ \\ \displaystyle \mathsf{ \left \{ {{-a + b = 2 (2)} \atop {2a + b = 8}} \right. }\\ \\ \\ \displaystyle \mathsf{ \left \{ {{-2a + 2b = 4} \atop {2a + b = 8}} \right. }\\ \displaystyle \mathsf{\rule{75}{0,7}}\\ \displaystyle \mathsf{3b = 12}\\ \\ \displaystyle \mathsf{b = \frac{12}{3}}\\ \\ \displaystyle \mathsf{b = 4}$

$\displaystyle \mathsf{-a + b = 2}\\ \\ \displaystyle \mathsf{b = 4}\\ \\ \displaystyle \mathsf{-a + 4 = 2}\\ \displaystyle \mathsf{-a = 2 - 4}\\ \displaystyle \mathsf{-a = -2 \: (-1)}\\ \displaystyle \mathsf{a = 2}$

$\displaystyle \mathsf{F(x) = ax + b}\\ \\ \displaystyle \mathsf{a = 2; b = 4}\\ \\ \displaystyle \mathsf{F(x) = 2x + 4}$

Resposta: F(x) = 2x + 4