Question

determine a lei da função do primeiro grau (-1, 2) e (2, -1)

Answer 1

Sabemos que a função do 1° grau é dada na forma:

$y~=~a.x+b$

Substituindo os pontos dados no modelo, achamos o seguinte sistema:

$\left\{\begin{array}{ccc}2&=&-1a+b\\-1&=&2a+b\end{array}\right\\\\\\Invertendo~as~equacoes~para~facilitar:\\\\\\\left\{\begin{array}{ccc}-1a+b&=&2\\2a+b&=&-1\end{array}\right\\\\\\Utilizando~o~metodo~da~adicao,~somamos~a~2^a~equacao~com\\o~negativo~da~1^a:\\\\\\(2a+b)-(-1a+b)~=~-1-2\\\\\\2a+b+a-b~=~-3\\\\\\3a~=~-3\\\\\\a~=~\frac{-3}{3}\\\\\\\boxed{a~=~-1}\\\\\\Substituindo~o~valor~de~"a"~em~uma~das~equacoes~para~achar~"b":\\\\\\-a+b~=~2\\\\\\-(-1)+b~=~2\\\\\\b~=~2-1$

$\boxed{b~=~1}$

Sendo assim, a função fica:

$f(x)~=~y~=~a.x+b\\\\\\\boxed{f(x)~=~y~=\,-x+1}$